To the best of my knowledge, the following constructions are used to express purpose in Latin:

  1. ut + [subjunctive clause]
  2. ad + [accusative gerund]
  3. ad + [accusative gerundive] + [accusative noun]
  4. [genitive gerund] + causā
  5. [genitive gerundive] + [genitive noun] + causā
  6. supine with verbs of motion
  7. (rare) infinitive with a select few verbs
  8. quī, quae, quod + [subjunctive clause]
  9. quo + [comparative adverb] + [subjunctive clause]

For someone approaching Latin from a strictly philological perspective, it's only really important to know that all of these constructions are used express purpose; it is not especially important for said someone to know when and where these constructions are used and when and where to prefer one over the other. I, however, am not simply approaching from a philological perspective; I want to be able to write (and eventually speak) Latin and do it well.

With all that said, when and where should each method of expressing purpose be used, being preferred over the others? Point six is exempt, obviously; it is clear from its description when and where it should be used.

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    You can also use [6] qui (quae, quod) and [7] quo + [comparative adverb, e.g. facilius], in either case followed by a subjunctive. – Tom Cotton Sep 7 '18 at 16:22
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    @TomCotton Thanks for the extra info; it has been added to the question! – Ethan Bierlein Sep 7 '18 at 16:35
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    One meaning of the future active infinitive is 'intending to x'; therefore, it can be used to express purpose. When paired with a form of esse, it can express the purpose either in a main clause or in a subordinate clause that's equivalent to a 'proper' purpose clause with ut/ne. It can also be used, without esse, just as a participle that's also equivalent to a subordinate clause. Pliny the Younger uses it this way quite often. – cnread Sep 7 '18 at 17:04
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    I might also consider the future participle for this purpose: domum redii dormiturus. – Joonas Ilmavirta Sep 8 '18 at 15:09
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    Just to clarify the list: I think [3] should be "ad + acc. noun + gerundive." In [4], the order is reversed and can also include a gerundive, i.e. [4a] "gen. gerund + causa" and [4b] "gen. noun + gerundive + causa" – brianpck Sep 9 '18 at 17:04

It's obvious from the list of constructions that this question is not going to have a simple answer. As ever, it all depends on context, style and personal preference.

There is a clear resumé of some of the options in "Latin Prose Composition", an elementary textbook by North & Hillard much used in England in previous centuries. Rule 18 states that "A relative with the subjunctive may express many adverbial meanings, especially a Purpose or a Consequence". Examples of Final and Consecutive clauses are given, but the appended Note is neatly illustrative:

"We thus have four ways of expressing purpose in Latin, viz. as in the following sentences :

(1  Legatos miserunt *ut pacem peterent*
(2) Legatos miserunt *qui pacem peterent*
(3) Legatos miserunt *ad pacem petendam*
    Legatos miserunt *pacis petendae causa*
(4) Legatos miserunt *pacem petitum*

"Occasionally also purpose is expressed by the future participle ;

*e.g.*  Legatos miserunt *pacem petituros* "

This covers most of your (amended) list. Missing still are :

causa + genitive (e.g. arma posuernt pacis causa), which does not specifically require a following gerund and quo with comparative adverb, followed by a subjunctive (e.g. arma posuerunt quo certius bellum finiretur).

Having cleared all that, I ought to answer your direct question. There is no "correct" or "preferred" means of expressing purpose in the sense for which you ask. Learning Latin prose composition is just like learning prose composition in any language: it is best picked up by becoming familiar with the writings of good authors. Who these might be in Latin was debated from Quintilian's time, through that of Priscian and right through to the Renaissance, when Humanist Latin was attempting to preserve and emulate the best kind of writing (it largely came down to Caesar, Cicero and Seneca, though not exclusively by any means). In short, there's no set of rules, hard or easy, that have to be followed — and to develop fluency only practice, practice and more practice, with a readiness to accept criticism and advice will do the trick!

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