To the best of my knowledge, the following constructions are used to express purpose in Latin:
- ut + [subjunctive clause]
- ad + [accusative gerund]
- ad + [accusative gerundive] + [accusative noun]
- [genitive gerund] + causā
- [genitive gerundive] + [genitive noun] + causā
- supine with verbs of motion
- (rare) infinitive with a select few verbs
- quī, quae, quod + [subjunctive clause]
- 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.