How did Jesus select the Apostles to witness the Transfiguration?

In the Wikipedia article on the Apostles, the twelve are said to always be listed in each of the Synoptic Gospels in the same groups of four. It seems likely that there was a hierarchy of disciples, with the group leaders being Peter, Philip, and James son of Alphaeus. That means that Peter and his brother Andrew, John and his brother, James son of Zebedee were part of one of Jesus’ three cells.

The raises the question, “Why was Andrew not included?”

The inclusion of Peter is obvious. He was selected as leader by Jesus.

John was “the disciple whom Jesus loved”. He lived longest and was the only gospel writer among the four. It was important to have an eyewitness account of the Transfiguration in the Bible.

James was the first apostle to be martyred. Perhaps this was an anticipatory reward for his sacrifice?

The transfiguration was to "change into a different form". In the gospel accounts, it was from a human/divine into a divine/human. They witnessed the transformation, the point of the incarnation.

Tertullian points out that by the mouths of three witnesses something is established, referring to Deut 19:15. See here. Hence, three apostles. And hence the naming of the bookends of the New Testament. Eyewitnesses to His glory.

Justin Martyr explains the renaming as a right of God being God, similar to renamings in the Old Testament.

And when it is said that He [Jesus Christ] changed the name of one of the apostles to Peter; and when it is written in the memoirs of Him that this so happened, as well as that He changed the names of other two brothers, the sons of Zebedee, to Boanerges, which means sons of thunder; this was an announcement of the fact that it was He by whom Jacob was called Israel, and Oshea called Jesus (Joshua), under whose name the people who survived of those that came from Egypt were conducted into the land promised to the patriarchs. And that He should arise like a star from the seed of Abraham, Moses showed beforehand when he thus said, ‘A star shall arise from Jacob, and a leader from Israel;’ and another Scripture says, ‘Behold a man; the East is His name.’ Accordingly, when a star rose in heaven at the time of His birth, as is recorded in the memoirs of His apostles, the Magi from Arabia, recognising the sign by this, came and worshipped Him. Dialogue with Trypho

Hence, the mission of Peter to open the doors to Jew and Gentile. Done and done.

So, given three witnesses, given the preexistence of Christ and proofs, who were Peter, James and John?

Peter was renamed "rock" and more importantly given the keys of the kingdom.

Now I say to you that you are Peter (which means ‘rock’),[fn] and upon this rock I will build my church, and all the powers of hell[fn] will not conquer it. And I will give you the keys of the Kingdom of Heaven. Whatever you forbid[fn] on earth will be forbidden in heaven, and whatever you permit[fn] on earth will be permitted in heaven.” Mt. 16:18-19

Peter opened the kingdom to Jew and Gentile.

Then Peter stepped forward with the eleven other apostles and shouted to the crowd, “Listen carefully, all of you, fellow Jews and residents of Jerusalem! Make no mistake about this. Acts 2:14

To Jew, and then to Gentile.

He is the one all the prophets testified about, saying that everyone who believes in him will have their sins forgiven through his name.” Acts 10:43

As to James and John, they were the first and last apostles to die. They were renamed sons of thunder, as in the voice of God.

The voice of thy [God] thunder was in the heaven: the lightnings lightened the world: the earth trembled and shook. Psalm 77:18

Between those bookends, the New Testament was written (and some believe fully compiled).

And therefore it [Hermas] ought indeed to be read; but it cannot be read publicly to the people in church either among the Prophets, whose number is complete, or among the Apostles, for it is after [their] time. Muratorian Fragment