Important Commentaries?

There are no important commentaries & sub-commentaries. The Buddha did not teach his Dhamma for there to be a necessity for commentaries & sub-commentaries. Commentaries are heretical to what the Buddha taught. If you place faith in commentaries & sub-commentaries then you do not have faith in the Buddha & the Dhamma. Instead, you have faith in other individuals, who often misunderstood the Dhamma. The Buddha taught:

The teaching is well explained by the Buddha—visible in the here & now, immediately effective, inviting inspection, relevant, so that sensible people can know it for themselves.

SN 16.3

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Monks, in this Teaching that is so well proclaimed by me and is plain, open, explicit and free of patchwork

MN 22

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Thus spoke the Venerable Ananda, but the Blessed One answered him, saying: "What more does the community of bhikkhus expect from me, Ananda? I have set forth the Dhamma without making any distinction of esoteric and exoteric doctrine; there is nothing, Ananda, with regard to the teachings that the Tathagata holds to the last with the closed fist of a teacher who keeps some things back.

DN 16

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In future time, there will be bhikkhus who will not listen to the utterance of such discourses which are words of the Tathāgata, profound, profound in meaning, leading beyond the world, connected with emptiness, they will not lend ear, they will not apply their mind on knowledge, they will not consider those teachings as to be taken up and mastered. On the contrary, they will listen to the utterance of such discourses which are literary compositions made by poets, witty words, witty letters, by people from outside [the Dhamma], or the words of disciples, they will lend ear, they will apply their mind on knowledge, they will consider those teachings as to be taken up and mastered. Thus, bhikkhus, the discourses which are words of the Tathāgata, profound, profound in meaning, leading beyond the world, connected with emptiness, will disappear.

SN 20.7

However, if you are that keen:

http://www.tipitaka.de/roman/atthakatha/index.html

http://www.tipitaka.de/roman/tika/index.html

in short

What are the Important Commentaries?

Buddha, his teams, and his teaching memorizers.

Everyone can read and teach without standard, but the Tipitaka Memorizers keep that standard. He can comment Tipitaka in standard like the Judge memorized the law and keeping adjudicate in law.

7 questions for this topic

1. What is the commentary?
2. Who are those teachers?
3. What are the Important Commentaries?
4. Who are their teams?
5. What is the qualification of the teams?
6. How to choose one?
7. What should the practitioner do to his teacher?

What is the commentary?

The commentary is the description from teachers.

Who are those teachers?

Buddha and his teams, the great disciple (Asītimahāsāvaka, Etadagga, Sakya Family, etc.)

What are the Important Commentaries?

Those teachers and their teams.

Everyone can read and teach without standard, but the Tipitaka Memorizers keep that standard. He can comment Tipitaka in standard like the Judge memorized the law and keeping adjudicate in law.

Who are their teams?

The noble one and the Tipitaka Memorizers.

What is the qualification of the teams?

From my answer here : How to find the right Dhamma teacher

in my opinion, the significant quality of a teacher is paṭisambhidā: because all ariya must have paṭisambhidā, at least in his kammaṭṭhāna. So he should have these qualities:

1. His teacher descent, he must derived from a tipitaka memorizer (buddha-sāvaka, suta-buddha; V.N. Mahāvagga Nissayamuccnakathā).
2. His enlightenment, he must achieved at least upacāra-samādhi and balava-vipassanā (4 paṭisambhidā; V.N. Mahāvagga Nissayamuccnakathā).
3. His tipitaka memory, he must graduated through at least nissayamuccaka-course (V.N. Pācittiyakaṇḍa Ovādakasikkhāpada's commentary).
4. His tipitaka understanding, he must not cut tipitaka off or make tipitaka conflict each other. Because tipitaka was memorized by single commentary teacher group at 1st saṅgāyanā, so it must be a single package that compatibility with each other (pro in tipitaka relation, dhamma-paṭisambhida&attha-paṭisambhidā).
5. His pali skill, he must understand pali in advance (nirutti-paṭisambhidā).
6. He must be a genius one (paṭibhāna-paṭisambhidā).

Furthermore, in tipitaka and commentary tradition, since mahākhandhaka of vinaya mahāvagga is completed authored by upāli in 1st saṇgāyanā, all layman's teachers must have all of these qualities, that concluded by upāli in bhikkhunovādakasikkhāpada's commentary (which I translate below as follows):

Qualities of nissayamuccaka-bhikkhu (teaching lay people)

1. Proficient to recite pāṭimokkha-pāli and to understand it's commentary.
2. Proficient to recite and to understand 4 bhāṇavāra (~1,000 syllable) of sutta and their commentary, to teach laymen on uposatha day.
3. Proficient to recite and to understand sutta for bhikkhu's life such as andhakavindasutta, mahālahulovādasutta, ambaṭṭhasutta, etc.
4. Proficient to recite and to understand sutta for teaching in 3 chances: banquet for saṅgha by layman (nidhikaṇdasutta), funeral ceremony (tirokuṭṭasutta), and auspicious ceremony (maṅgalasutta).
5. Enough understand to judge/to decide about saṇgha's ceremony such as uposatha, pavāraṇā, etc.
6. Proficient to recite and to understand his kammaṭṭhānā throughout the nibbāna-course.
7. 5 years experience in monk hood as a monk.

Qualities of bhikkuparisūpaṭṭhāpaka-bhikkhu (teaching bikkhus)

If above layman's teachers want to teach bhikkhus (ūpajjhā-ācāriya, nissaya-ācāriya), they must increase their skill level to all of the following qualities.

These are for abhivinaya teaching:

1. Proficient to recite mahāvibhagha and bhikkhunivibhaṅga (first 3 books of thai 45 books pali-tipitaka) of vinaya-pitaka-pali. At least, he can relay with the other 3 bhikkhu. Proficient to understand it's commentary, too.
2. Proficient to recite all saṇgha's ceremony in vinaya-pitaka mahāvagga and julavagga.
3. Proficient to recite 14 vatta in vattakhandhaka.

These are for abhidhamma (kammaṭṭhāna) teaching:

4. Proficient to recite one of this suttanta-pali: mūlapaṇṇassa (1st/3 parts of M.N.) for student in M.N. faculty, mahāvagga (2nd/3 parts of D.N.) for student in D.N. faculty, sagāthavagga+nidānavagga+khandhavāravagga of S.N. or mahāvagga of S.N. for student in S.N. faculty, before half of A.N. or after half of A.N. or ekakanipāta+dukanipāta of A.N. for student in A.N. faculty, jātaka+commentary (because kammaṭṭhāna was described in commentary) for student in jātaka faculty.

Qualities of bhikkunovdaka-bhikkhu (teaching bhikkunīs)

If above layman's teachers want to teach bhikkhunī, they must increase their skill level to all of these qualities:

1. Proficient to recite whole tipitaka-pali and commentary-pali. Or at least, he still must recite whole tipitaka, but he can recite just one commentary of suttanta, first 4 parts of commentary of 7 parts of abhidhamma. However, vinaya-commentary is what he must recite it all.

Reference: tipitaka and commentary of vinaya pācittiyakaṇḍa bhikkhunovādakasikkhāpada and vinaya mahāvagga mahākhandhaka.

(I still find it difficult to reference the tipitaka and commentary using english resources: there's no translation, very long pages, confused categories, cutting some parts off the tipitaka, cutting commentary off from pali canon, etc.)

Related topic: Should Lay Buddhists Teach the Dhamma?

How to choose one?

62. Because of the words beginning, "Ananda, it is owing to my being a good friend to them that living beings subject to birth are freed from birth" (S I 88), it is only the Fully Enlightened One who possesses all the aspects of the good friend. Since that is so, while he is available only a meditation subject taken in the Blessed One's presence is well taken.

    But after his final attainment of Nibbana, it is proper to take it from anyone of the eighty great disciples still living. When they are no more available, one who wants to take a particular meditation subject should take it from someone with cankers destroyed, who has, by means of that particular meditation subject, produced the fourfold and fivefold jhana, and has reached the destruction of cankers by augmenting insight that had that jhana as its proximate cause.

63. But how then, does someone with cankers destroyed declare himself thus: "I am one whose cankers are destroyed?" Why not? He declares himself when he knows that his instructions will be carried out. Did not the Elder Assagutta [99] spread out his leather mat in the air and sitting cross-legged on it explain a meditation subject to a bhikkhu who was starting his meditation subject, because he knew that that bhikkhu was one who would carry out his instructions for the meditation subject?

64. So if someone with cankers destroyed is available, that is good. If not, then one should take it from a non-returner, a once-returner, a stream-enterer, an ordinary man who has obtained jhana, one who knows three Pitakas, one who knows two Pitakas, one who knows one Pitaka, in descending order [according as available]. If not even one who knows one Pitaka is available, then it should be taken from one who is familiar with one Collection together with its commentary and one who is himself conscientious. For a teacher such as this, who knows the texts, guards the heritage, and protects the tradition, will follow the teachers' opinion rather than his own. Hence the Ancient Elders said three times, "One who is conscientious will guard it."

65. Now, those beginning with one whose cankers are destroyed, mentioned above, will describe only the path they have themselves reached. But with a learned man, his instructions and his answers to questions are purified by his having approached such and such teachers, and so he will explain a meditation subject showing a broad track, like a big elephant going through a stretch of jungle, and he will select suttas and reasons from here and there, adding [explanations of] what is suitable and unsuitable. So a meditation subject should be taken by approaching the good friend such as this, the giver of a meditation subject, and by doing all the duties to him.

    Chapter III Taking a Meditation Subject page 94

    cr. http://www.bps.lk http://www.accesstoinsight.urg

What should the practitioner do to his teacher?

66. If he is available in the same monastery, it is good. If not, one should go to where he lives.

    When [a bhikkhu] goes to him, he should not do so with feet washed and anointed, wearing sandals, with an umbrella, surrounded by pupils, and bringing oil tube, honey, molasses, etc.; he should do so fulfilling the duties of a bhikkhu setting out on a journey, carrying his bowl and robes himself, doing all the duties in each monastery on the way, with few belongings, and living in the greatest effacement. When entering that monastery, he should do so [expecting nothing, and even provided] with a tooth-stick that he has had made allowable on the way [according to the rules]. And he should not enter some other room, thinking, "I shall go to the teacher after resting awhile and after washing and anointing my feet, and so on."

67. Why? If there are bhikkhus there who are hostile to the teacher, they might ask him the reason for his coming and speak dispraise of the teacher, saying, "You are done for if you go to him"; [100] they might make him regret his coming and turn him back. So he should ask for the teacher's dwelling and go straight there.

68. If the teacher is junior, he should not consent to the teacher's receiving his bowl and robe, and so on. If the teacher is senior, then he should go and pay homage to him and remain standing. When told, "Put down the bowl and robe, friend," he may put them down. When told, "Have some water to drink," he can drink if he wants to. When told, "You may wash your feet," he should not do so at once, for if the water has been brought by the teacher himself, it would be improper. But when told "Wash, friend, it was not brought by me, it was brought by others," then he can wash his feet, sitting in a screened place out of sight of the teacher, or in the open to one side of the dwelling.

69. If the teacher brings an oil tube, he should get up and take it carefully with both hands. If he did not take it, it might make the teacher wonder, "Does this bhikkhu resent sharing so soon?" but having taken it, he should not anoint his feet at once. For if it were oil for anointing the teacher's limbs, it would not be proper. So he should first anoint his head, then his shoulders, etc.; but when told, "This is meant for all the limbs, friend, anoint your feet," he should put a little on his head and then anoint his feet. Then he should give it back, saying when the teacher takes it, "May I return this oil tube, venerable sir?"

70. He should not say, "Explain a meditation subject to me, venerable sir" on the very day he arrives. But starting from the next day, he can, if the teacher has a habitual attendant, ask his permission to do the duties. If he does not allow it when asked, they can be done when the opportunity offers. When he does them, three tooth-sticks should be brought, a small, a medium and a big one, and two kinds of mouth-washing water and bathing water, that is, hot and cold, should be set out. Whichever of these the teacher uses for three days should then be brought regularly. If the teacher uses either kind indiscriminately, he can bring whatever is available.

71. Why so many words? All should be done as prescribed by the Blessed One in the Khandhakas as the right duties in the passage beginning: "Bhikkhus, a pupil should perform the duties to the teacher [101] rightly. Herein, this is the right performance of duties. He should rise early; removing his sandals and arranging his robe on one shoulder, he should give the tooth-sticks and the mouth-washing water, and he should prepare the seat. If there is rice gruel, he should wash the dish and bring the rice gruel" (Vin I 61).

72. To please the teacher by perfection in the duties he should pay homage in the evening, and he should leave when dismissed with the words, "You may go." When the teacher asks him, "Why have you come?" he can explain the reason for his coming. If he does not ask but agrees to the duties being done, then after ten days or a fortnight have gone by he should make an opportunity by staying back one day at the time of his dismissal, and announcing the reason for his coming; or he should go at an unaccustomed time, and when asked, "What have you come for?" he can announce it.

73. If the teacher says, "Come in the morning," he should do so. But if his stomach burns with a bile affliction at that hour, or if his food does not get digested owing to sluggish digestive heat, or if some other ailment afflicts him, he should let it be known, and proposing a time that suits himself, he should come at that time. For if a meditation subject is expounded at an inconvenient time, one cannot give attention.

    This is the detailed explanation of the words "approach the good friend, the giver of a meditation subject."

    Chapter III Taking a Meditation Subject page 94

    cr. http://www.bps.lk http://www.accesstoinsight.urg

In my opinion commentaries and sub commentaries are important. Even the Tipitaka is a tabulation by certain Arahants. In any case, I ask a similar question in the Dhamma Wheel.

https://dhammawheel.com/viewtopic.php?f=36&t=35754