Interesting question. Here's a direct quote from Wikipedia:

Arius appealed to Scripture, quoting verses such as John 14:28: "the Father is greater than I", as well as Colossians 1:15: "the firstborn of all creation."

Source: Arius on Wikipedia

These two verses were mentioned in another answer but I wanted to quote them from the wiki article and link to it. The OP mentions Revelation 3:14 as well. I've not come across that in any of the few of Arius' writings that are left. But it doesn't mean he didn't try to use it!

I'm really quite sure that he (and many others) appealed to Proverbs chapter 8, though. I'll see if I can find a quote.

This is a difficult question to give a simple straightforward answer. Firstly, regardless on your feelings regarding his interpretations, Arius was clearly well versed in much of scripture, so anything short of "all of scripture" would be a slightly inaccurate response. Secondly, we don't have much in the way of direct sources of his own writing. Most of the primary sources that we have today for Arius' actual teaching are not really primary at all. Many of them are from second or third-party contemporary sources speaking about Arius and his teachings.

If you are really interested, I would strongly suggest that you get a copy of the book called The Search for the Christian Doctrine of God by R. P. C. Hanson. It can be difficult to find, but it will be well worth your time to find it. It's the best study, in the English language, of the primary sources surrounding the Arian controversy of which I am aware. It covers in great detail, among other things, the Biblical arguments used by Arius and others. Some of them are based on specific proof-verses, as you are requesting, whereas some are more conceptual, being based on the comparison of multiple passages.

Here is a list of scriptures that Arius apparently used to support his doctrine that there was a time when the Son of God did not exist.

Alexander expressly notes that the Arians appeal to Scripture in support of their doctrine, and Athanasius says that the Thalia contained passages of Scripture.52 The passages so frequently cited later on by the Arians; Deut. VI. 4, XXXII. 39; Prov. VIII. 22; Ps. XLV. 8; Mt. XII. 28; Mk. XIII. 32; Mt. XXVI. 41, XXVIII. 18; Lk. II. 52, XVIII. 19; John XI. 34, XIV. 28, XVII. 3; Acts II. 36; 1 Cor. I. 24, XV. 28; Col. I. 15; Philipp. II. 6 f.; Hebr. I. 4, III. 2; John XII. 27, XIII. 21; Mt. XXVI. 39, XXVII. 46, etc., will thus already have been used by Arius himself. -Harnack-

As well, Arius linked scripture's Wisdom as the Son. -ibid-

It may help to understand the background of the controversy. In the persecution about 175, certain Christians denied Christ in order to remain alive. Theodosius invented the theory that Christ was a man of sorts, not divine like God. Thus he would say he did not deny God, but a man.

That teaching was picked up by Paul of Samosata. It was then developed more by Arius.

Introduction

The RH-references in this article are to the 1981 book by RPC Hanson - The Search for the Christian Doctrine of God - The Arian Controversy 318-381 - probably the most comprehensive and reliable description of the Arian Controversy available to us today.

The RW-references are to the 2001 book by Rowan Williams. - Arius, Heresy & Tradition, 2001 - an extremely valuable discussion of Arius' teachings. 

It is often claimed that Arius described the Son of God as a created being. It is the purpose of this article to show that that is a distortion of Arius’ theology.

1 God’s Only Direct Creation

Firstly, in Arius' theology, the Son is the only being ever to be brought forth directly by the Father. All other beings were brought forth by the Son. For example:

He is “the product of the Father” (RH, 7); “alone has been given existence by the Father” (RH, 8).

“He has been produced directly without mediation by God, and everything else has come into being through his mediation” (RH, 102).

“Nor does he live a life comparable to those things which were produced through him, but he has been brought forth alone from the Father himself and is Life in himself” (RH, 56; John 5:26).

Hanson concluded: “This direct creation means that the Son has nobody like him; the Arians' favourite title for the Son was unigenitus (only-begotten, John 1:4, 18; 3:16)” (RH, 102).

2 In God’s Presence

Secondly, the Arians taught that the Son is the only being who is able to endure direct contact with God. All other beings will be consumed by God’s presence:

One prominent Arian in Arius’ day (Asterius) explained that “when God desired that created nature should come into existence, he saw that nature could not endure his direct hand and so 'he initially makes and created, himself sole, a sole Being, and calls this Son and Word'; consequently, once this mediating Being had come into existence, the rest could be created.” (RH, 100)

“Demophilus, the last Arian bishop of Constantinople before the advent of Theodosius (AD 380), [says] God … 'could not come in contact with the creation which he intended to make, for he would have been under the necessity either of making everything gods so as to be worthy of him, or else everything would have disintegrated by contact with him. So the Son of God had to become a mediator between God and the things created by him.'” (RH, 101)

In this theory, following Asterius’ argument, the Son is the only Being who is able to endure direct contact with God. This makes an infinite distinction between the Son and the created universe.

This argument may sound strange to a modern ear, but is was the church's standard explanation of the Son of God when the Arian Controversy began. See - The Apologists.

3 Not part of this Universe

Thirdly, Arius described the Son as not part of this universe:

If the Son created all things (the universe), then He is not part of this universe.

Furthermore, Arius and the Arians claimed time and again that the Son was begotten “before times and before aeons” (RH, 7). In other words, the Son was begotten before time even existed. If we argue that time began when the universe was brought into being, the Son originates from that which exists beyond the time, space, and matter of this universe; He comes from the unfathomable infinity beyond this finite universe.

4 Our God

Fourthly, the Arians considered the Son to be their God. For example, “Ulfilas, bishop of the Goths,” described the Son as:

“Our Lord and God, artificer (craftsman) and maker of the whole creation, who has nobody like him” (RH, 105).

They described the Son as “our God” because:

Firstly, the Son created us: “The Father is the origin of everything made, but the Son brings everything into actual existence” (RH, 103).

Secondly, God is invisible, meaning that created beings cannot experience God directly. Only His Son is able to experience God directly. Our experience of God is limited to His Son.

Thirdly, in all things, the Logos is the intermediary and mediator between God and creation. Whatever we receive from God, we receive through the Son of God. He has all authority in heaven and on earth. And whatever worship we give to God, we give to Him through His Son.

These concepts create an infinite distinction between the Son and the created things. It causes a hierarchy in which the Son is above all other beings. In practice, He is the God for all other beings. For us, He is God. He is our God, just like the Father is His God (e.g., Rev 1:6; 3:2, 12)

5 Synonyms

Fifthly, for us, today, when we speak about Jesus Christ, there is a clear distinction between "created" and "begotten," but at the beginning of the fourth century, when talking about Jesus Christ, all Christians used the words “begotten” and “created” as synonyms. Richard Hanson confirms this:

(1) “Christians had long been accustomed to interpret the figure of Wisdom in the Wisdom literature of the Old Testament as a reference to the preexistent Christ” (RH, 20; cf. RH 8). Consequently, when Proverbs 8 describes Wisdom's generation with phrases such as "possessed," "established, and "brought forth," all Christians in Arius' day understood that as describing the Son of God:

• Proverbs 8:22 “The LORD possessed me at the beginning of His way … 23 “From everlasting I was established … 25 “Before the mountains were settled, … I was brought forth;

(2) “In the middle of the third century Dionysius, bishop of Alexandria; produced in a treatise an account of the Son as created” (RH, 872). This was an important bishop in the same city in which Arius lived, and Arius was born (c. 256) while Dionysius still was writing.

(3) Hanson adds that, in the time of Origen, in the third century, “nobody distinguished 'having come into existence' from 'begotten'” (RH, 63).

Consistent with Tradition

This means that Arius and his supporters were consistent with tradition when they used "created" as a synonym for "begotten." The following is an example of how they used these words as synonyms:

“He [the Father of Christ] created and begot, made and founded the Only-begotten God.”  (RH, 105; cf. RH, 6, 8, 30, 90).

The point is that must interpret Arius’ words using the meanings that words had then; not against the meanings that these words have today.

Innovation

But it also means, when the Nicene Creed uses these words as opposites in the phrase "begotten not made," that that was a new development. In the conventional account of the Arian Controversy, Arius’ theology was a break from the orthodoxy. However, it was the other way around: The Arians were the traditionalists and the Nicene Creed was an innovation:

Rowan Williams refers to “the radical words of Nicaea” (RW, 236) (referring particularly to the word h*m*ousios) as “conceptual innovation” (RW, 234-5). And Hanson described h*m*ousios as one of the "new terms borrowed from the pagan philosophy" (RH, 846).

Hanson concludes: “There is no doubt ... that the pro-Nicene theologians throughout the controversy were engaged in a process of developing doctrine and consequently introducing what must be called a change in doctrine” (RH, 872). “The Arians failed just because they were so inflexible, too conservative, not ready enough to look at new ideas” (RH, 873).

Arian Response

The Nicene Creed defines “created” and “begotten” as opposites and interprets “begotten” fairly literally, saying that it means that the Son came out of the substance of the Father. It was to object to this that the Arians argued that we should not interpret “begotten” literally because the Son’s generation from the Father is ineffable (indescribable and incomprehensible). For example:

Eusebius of Nicomedia, who “was a supporter of Arius as long as Arius lived,” wrote as follows: “'(There is) One, the Unoriginated and One produced by him … produced … not only indescribable by word but also incomprehensible by thought not only of men but also of all those who are superior to men” (RH, 30).

“Eusebius, bishop of Caesarea … an early supporter of Arius” (RH, 46), wrote that the Son was “begotten … by processes which are to us ineffable and mysterious and altogether unknowable” (RH, 56).

Malicious Distortion

In conclusion, Arius clearly taught that no other creature is comparable to Him: “He is only-begotten God and he is different from any others” (RH, 14). Consequently, the later Arians were “not happy with the use of the term 'created', because this suggests that the Son is to be classified with other created things” (RH, 102).

It was their opponents, particularly Alexander and Athanasius, who decided to single out and emphasize the word “created” in the writings of the Arians. For example, they would write that, for the Arians:

“The Son is a creature” and, “He is one of the products” (RH, 16 - Alexander).

“He is properly 'of those who come into existence and are created” (RH, 14 – Athanasius’ paraphrasing).

“When he came into existence, he was then such as is every man: because they say that God made everything out of non-existence” (RH, 17 - Alexander).

“We are able to become the sons of God as he is, for it is written, 'I have begotten sons and I have exalted them' (Isa 1:2 LXX)” (RH, 17 - Alexander).

Alexander and Athanasius did their best to present Arius’ Son of God as a normal created being. Therefore, since Arius wrote that the Son created all things, Alexander, to describe Arius’ Son as a normal creature, de-emphasized the Son's role in creation:

“He was made for our sake, in order that God should create us through him as through an instrument” (RH, 16 - Alexander).

On pages 104-105, Rowan Williams discusses Athanasius’ quotes of Arius’ works and shows how Athanasius distorted Arius’ words. He concludes:

“The Son is repeatedly assimilated to the level of other creatures, and the phrases ‘like us’ and ‘like all others' recur. The Arius who wrote to Alexander that the Son was a 'perfect creature, yet not as one among the creatures, a begotten being, yet not as one among things begotten … is eager to avoid any suggestion that the Son is simply ‘like all others'.” (RW, 104)

Williams says that Athanasius applied “unscrupulous tactics in polemic and struggle” (RW, 239). Hanson concurs that Athanasius' writings maliciously distorts Arius’ message. He wrote:

“Athanasius, a fierce opponent of Arius … certainly would not have stopped short of misrepresenting what he said” (RH, 10)

“Athanasius … may be suspected of pressing the words maliciously rather further than Arius intended” (RH, 15).

“He (Arius) did not teach (as his opponents maliciously alleged) that the Son was no greater than the locust or caterpillar” (RH, 20).

All this was known in Arius’ day. For example, in a letter, Eusebius of Caesarea took Alexander “to task for unjustly accusing Arius and his friends of teaching that 'the Son has come into existence from non-existence like one of the mass', whereas what they had actually said was that the Son was 'a perfect creature, but not as one of the creatures'” (RH, 56-57).

However, Athanasius’ message has become accepted in the church as truth because the “conventional account of the Controversy … stems originally from the version given of it by the victorious party.” (RPC Hanson) But Hanson adds that this “is now recognised by a large number of scholars to be a complete travesty.”

There is no evidence that Arius was influenced by Revelation 3:14 or Psalms 8:5-6, but he appealed to Bible verses such as Jesus saying that the father is "greater than I" (John 14:28), and "The Lord created me at the beginning of his work" (Proverbs 8:22). He was also influenced by Origen.

Richard Smoley says in Forbidden Faith, page 45, Origen held an emanationist view of the relation between the Father and the Son, which is sometimes called 'subordination of the divine Persons”. According to Origen, the Father eternally generates the Son, even though the Son was not created in time. To later theologians, Origen's emanationism sounded enough like Arius' teaching to be condemned by association.

Neither side, Arian nor Trinitarian, could prove its case convincingly, but Alexander, bishop of Alexandria, declared heretical the views of Arius and had him and the clergy who supported him, excommunicated. In order to fully exclude Arius, Alexander had the wording that Christ was “of one being with God” adopted at Nicaea. (Elaine Pagels, Beyond Belief, page 174).

Edward Gibbon says in The Decline and Fall of the Roman Empire (D. M. Low abridgement, page 320) Constantine, wishing to bring the dispute between Alexander and Arius to an end, issued an absolute command that Arius should be solemnly admitted to the communion in the cathedral of Constantinople. On the day which had been fixed for the triumph of Arius, he expired. Gibbon comments that the circumstances of his death might raise a suspicion that the orthodox saints had contributed more than their prayers to deliver the Church from their most formidable enemy, Arius.

In the early fourth century, many Christians were divided over how best to understand the relationship between God and Jesus. Emperor Constantine called for an ecumenical council of bishops to settle the matter: the Council of Nicea, in 325 AD. The result was a condemnation of 'the Arian heresy'.

Letter to Emperor Constantine

A few years later, in 327 AD, Arius and his ally Euzoïus addressed a letter to Emperor Constantine to explain what their beliefs were. (Presumably, they didn't trust their trinitarian opponents to accurately represent them.) Arius wrote:

We believe in one God the Father Almighty, and in the Lord Jesus Christ his son, who was begotten of him before all ages, God the Word through whom all things were made, both things in heaven and on earth; who descended, and became human, and suffered, and rose again, ascended into heaven, and will again come to judge the living and the dead. We believe also in the holy spirit, and in the resurrection of the flesh, and in the life of the coming age, and in the kingdom of the heavens, and in one catholic church of God, extending from one end of the earth to the other.

This faith we have received from the holy gospels, in which the Lord says to his disciples, ‘Go and teach all nations, baptizing them in the name of the Father, and of the son, and of the holy spirit.’ If we do not so believe and do not truly receive the Father, the son, and the holy spirit, as the whole catholic church and the holy scriptures teach (in which we believe in every respect), may God judge us both now, and in the coming judgment.

In the second paragraph cited above, Arius included Matthew 28.19, a verse often used to argue for the trinity. By citing this passage, Arius was showing that he was not ignorant of its existence, and thus implicitly that he did not believe it taught a trinitarian theology.

The first paragraph above, Arius presents the beliefs of his group in the form of a creed. (The shape of this creed was possibly in direct response to the Nicene Creed that had been drafted at the council.) Notably, Arius' creed begins with an apparent allusion to 1 Corinthians 8.6 ('We believe in God the Father Almighty, and in the Lord Jesus Christ his son'). Because Paul identifies each 'God the Father' and 'the Lord Jesus Christ', Arius seems to have taken this as a hard distinction between the two. This is a starting point, but very little else is readily discernible from this letter.

Letter to Alexander

A much more accessible letter to work with would be Arius' letter to Alexander circa 320 AD. Alexander was the bishop of Alexandria, and one of Arius' opponents. In this letter, Arius wrote his group's beliefs:

We acknowledge one God, alone unbegotten, alone everlasting, alone without beginning, alone true, alone having immortality, alone wise, alone good, alone sovereign, judge, governor, and provider of all, unalterable and unchangeable, just and good, God of the Law and the Prophets and the New Covenant. Who begat an only-begotten son before time and the ages, through whom he made both the ages and all that was made; who begot him not in appearance, but in reality; and that he made him subsist at his own will, unalterable and unchangeable, the perfect creature of God, but not as one of the creatures; offspring, but not as one of the other things begotten.

Now we have something to work with. Arius provides a dense cluster of allusions to Old and New Testament scripture, giving us a much stronger sense of his approach to the Bible as a whole:

• "We acknowledge one God" — Presumably Deuteronomy 6.4 would be the ultimate origin of his point, but the phrase 'one God' is scattered throughout both Old and New Testaments.
• "Alone unbegotten" — Psalm 2.7 would be the ultimate origin of this, as this psalm was popularly associated with Jesus (e.g. Acts 13.33; Hebrews 1.5). Arius took this to mean that, if Jesus was 'begotten', he must have had a beginning. This would go on to become one of the chief arguments used by Arius and those in agreement with him.
• "Alone everlasting" — Possibly Isaiah 40.28 (Isaiah 40-55 has numerous examples of monotheistic proclamations), or perhaps Romans 16.26.
• "Alone true" — John 17.3, where in prayer Jesus identifies the Father as 'the only true God'. While the Hebrew term 'elohim and the Greek term theos may be applied in various ways to human, angelic, or even demonic entities, Arius took this verse to mean that the Father alone could truly be identified with the term 'God', and thus not Jesus.
• "Alone having immortality" — This is an explicit reference to 1 Timothy 6.15-16, where the author of the epistle wrote that God 'alone has immortality' (cf. 1 Timothy 1.17). Since God (whom Arius had already identified one-to-one with 'the Father') is alone immortal, Arius reasoned that Jesus was not immortal in the same sense, and thus not 'God'.
• "Alone wise" — Romans 16.27, where Paul concludes his letter with a benediction 'to the only wise God forevermore through Jesus Christ!'
• "Alone good" — Mark 10.18. Arius read this to mean that Jesus denied being God.
• "Alone sovereign, judge, and governor" — 1 Timothy 6.15, where the author of the epistle says God is 'the only sovereign, the king of kings, and lord of lords' (cf. 1 Timothy 1.17).

Later in the same letter, Arius wrote:

Therefore he thus has his being from God; and glories, and life, and all things have been given over to him; in this way God is his beginning. For he is over him, as his God and being before him. But if the expressions 'from him' and 'from the womb' and 'I came from the Father, and I have come', are understood by some to mean that he is part of him, one in essence or as an emanation, then the Father is, according to them, compounded and divisible and alterable and material, and as far as their belief goes, the incorporeal God endures a body.

Here Arius explicitly cites three passages to distinguish Jesus as having a beginning and origin, in contrast to 'the eternal God'. Presumably, the passages Arius is quoting from were:

• "from him" — John 6.46.
• "from the womb" — Psalm 110.3.
• "I came from the Father, and I have come" — John 16.28.

Thalia

Arius also wrote a poem titled Thalia, though it is uncertain when the poem was written, or even if what we have is an authentic copy of the text. (All we have is provided by his opponents.) The existing text does allude to Proverbs 8.22-25, and possibly also combines it with Revelation 3.14:

He who is without beginning made the Son a beginning of created things

and

Wisdom came to be Wisdom by the will of the Wise God
. . .
The one who is superior is able to beget one equal to the Son

Summary

We could continue, but I think this is enough to demonstrate the key passages Arius relied on, as well as his general hermeneutic to the scriptures. Whenever Arius saw a biblical author speaking of 'one God', or that God 'alone' had an attribute, he took this as antithetical to a trinitarian theology. Whenever Arius saw a biblical author distinguishing between 'God' and 'Jesus', he took this to mean Jesus was not himself God.