Importance of good moral conduct

Would all Buddhists agree with this?

Another translation could say "remorse" instead of "regret".

I think there are other important reasons too for moral conduct (e.g. metta and sukha, perhaps especially for laypeople); but that "freedom from remorse" is canonically how it relates to the beginning of meditation (perhaps especially for the ordained); e.g. this from the Vinaya:

Discipline is for the sake of restraint,
restraint for the sake of freedom from remorse,
freedom from remorse for the sake of joy,
(etc.)

There's similar in a sutta, see The rewards of virtue.

Texts I've read suggest that good moral conduct should (perhaps must) be practised first.

Good moral conduct is extremely important because, although it, in itself, does not bring the goal, the goal cannot be reached without it.

If a bhikkhu should wish: ‘May I be dear and agreeable to my companions in the holy life, respected and esteemed by them,’ let him fulfil the precepts, be devoted to internal serenity of mind, not neglect meditation, be possessed of insight, and dwell in empty huts.

“If a bhikkhu should wish: ‘May I be one to obtain robes, almsfood, resting place, and medicinal requisites,’ let him fulfil the precepts…

“If a bhikkhu should wish: ‘May the services of those whose robes, almsfood, resting place, and medicinal requisites I use bring them great fruit and benefit,’ let him fulfil the precepts…

“If a bhikkhu should wish: ‘When my kinsmen and relatives who have passed away and died remember me with confidence in their minds, may that bring them great fruit and great benefit, ’ let him fulfil the precepts…

“If a bhikkhu should wish: ‘May I become a conqueror of discontent and delight, and may discontent not conquer me; may I abide transcending discontent whenever it arises,’ let him fulfil the precepts…

“If a bhikkhu should wish: ‘May I become a conqueror of fear and dread, and may fear and dread not conquer me; may I abide transcending fear and dread whenever they arise,’ let him fulfil the precepts…

“If a bhikkhu should wish: ‘May I become one to obtain at will, without trouble or difficulty, the four jhānas that constitute the higher mind and provide a pleasant abiding here and now,’ let him fulfil the precepts…

“If a bhikkhu should wish: ‘May I contact with the body and abide in those liberations that are peaceful and immaterial, transcending forms,’ let him fulfil the precepts…

“If a bhikkhu should wish: ‘May I, with the destruction of three fetters, become a stream-enterer, no longer subject to perdition, bound for deliverance, headed for enlightenment,’ let him fulfil the precepts…

“If a bhikkhu should wish: ‘May I, with the destruction of three fetters and with the attenuation of lust, hate, and delusion, become a once-returner, returning once to this world to make an end of suffering,’ let him fulfil the precepts…

“If a bhikkhu should wish: ‘May I, with the destruction of the five lower fetters, become due to reappear spontaneously in the Pure Abodes and there attain final Nibbāna, without ever returning from that world,’ let him fulfil the precepts…

“If a bhikkhu should wish: ‘May I wield the various kinds of supernormal power: having been one, may I become many; having been many, may I become one; may I appear and vanish; may I go unhindered through a wall, through an enclosure, through a mountain as though through space; may I dive in and out of the earth as though it were water; may I walk on water without sinking as though it were earth; seated cross-legged, may I travel in space like a bird; with my hand may I touch and stroke the moon and sun so powerful and mighty; may I wield bodily mastery, even as far as the Brahma-world,’ let him fulfil the precepts…

“If a bhikkhu should wish: ‘May I, with the divine ear element, which is purified and surpasses the human, hear both kinds of sounds, the divine and the human, those that are far as well as near,’ let him fulfil the precepts…

“If a bhikkhu should wish: ‘May I understand the minds of other beings, of other persons, having encompassed them with my own mind. May I understand a mind affected by lust as affected by lust and a mind unaffected by lust as unaffected by lust; may I understand a mind affected by hate as affected by hate and a mind unaffected by hate as unaffected by hate; may I understand a mind affected by delusion as affected by delusion and a mind unaffected by delusion as unaffected by delusion; may I understand a contracted mind as contracted and a distracted mind as distracted; may I understand an exalted mind as exalted and an unexalted mind as unexalted; may I understand a surpassed mind as surpassed and an unsurpassed mind as unsurpassed; may I understand a concentrated mind as concentrated and an unconcentrated mind as unconcentrated; may I understand a liberated mind as liberated and an unliberated mind as unliberated,’ let him fulfil the precepts…

“If a bhikkhu should wish: ‘May I recollect my manifold past lives, that is, one birth, two births…as Sutta 4, §27…Thus with their aspects and their particulars may I recollect my manifold past lives,’ let him fulfil the precepts…

“If a bhikkhu should wish: ‘May I, with the divine eye, which is purified and surpasses the human, see beings passing away and reappearing, inferior and superior, fair and ugly, fortunate and unfortunate; may I understand how beings pass on according to their actions thus:’…as Sutta 4, §29…let him fulfil the precepts…

“If a bhikkhu should wish: ‘May I, by realising for myself with direct knowledge, here and now enter upon and abide in the deliverance of mind and deliverance by wisdom that are taintless with the destruction of the taints,’ let him fulfil the precepts, be devoted to internal serenity of mind, not neglect meditation, be possessed of insight, and dwell in empty huts.

MN 6

It leads to non-regret, one who has non-regret gets serene one who gets serene gets concentrated

So it acts as foundation for concentration, meditative methods use and further develope that same concentration faculty which in turn supports developement of discernment and wisdom.

Sutta references: AN 10.2 & AN 11.2