To find what wiring type you can use, you need to look at each wiring method article and start with the Uses Permitted and Uses Not Permitted sections. Pick the method you want to use (easiest, cheapest, whatever) and see if it works. If you start with NM cable, look at 334.10 (Uses Permitted). It helps if it is associated with a dwelling, e.g. on residential property or a pergola for an apartment or condo. If not, you can still use NM as long as its concealed behind a 15 minute rated finish material. Looking at 334.12 (Uses Not Permitted) part (B), you can't use NM in damp or wet locations. A covered pergola would not be a wet area directly under the ceiling or roof. But the definition of damp area is vague and the inspector could maybe call it a damp area. If the pergola has enclosed sides, that could help. NM cable also can't be subject to physical damage which is also a subjective definition, but being high up can often get you past that.
So you could decide to forgo NM and try UF cable (see article 340 for details). It is OK to use in damp and wet areas. But if this pergola is not associated with a dwelling type building, then you may not want to have to mess with a 15 minute rated finish. So go to your next choice which could maybe be MC cable (article 330). Probably no show stoppers with MC cable.
Finally, remember that the NEC is a permissive document. You can use a wiring method any way for anything unless there is a prohibition against it. So Uses Not Permitted is typically the important thing to look at and not something missing in Uses Permitted. Uses Permitted typically sticks some caveats on a given technique (e.g. you can do it this way if you also do XXX).
