I am looking for a Latin adjective — or several adjectives if no single one is enough — meaning "main". I might want to talk about a main building or the main idea of a theory. The only suitable adjective I know is principalis, but is this the best choice and are there other words I should know? Fore example, aedificium principale sounds fine, but I don't know if this is the best choice. In some languages one can use the noun "head" in this meaning (German "haupt-" and Finnish "pää-", for example), but the corresponding Latin adjective capitalis seems inappropriate.
There isn't much beyond the words you have indicated, which are already satisfactory, but I assume that you would like a bit more scope for expression, for which both superus in its degrees of comparison and caput can be useful in working round the problem.
The simple adjective superus indicates a higher position, as in pars supera, 'the part above', or 'the upper part' etc, while Its comparative superior can be used to describe condition, number or quantity. By manipulating the context, either can suggest 'main'.
The superlative, formally superrimus, is more familiar in its shortened form summus (and superus is also found, though I believe its use is more often poetical). It expresses the highest, most exalted, topmost and so on and it is also better translated in some circumstances as 'main'. In particular, summus is used substantively as in summa (sc. res) the main point, and adjectivally as in summa rerum (though the usage may exist, I have never seen summarum rerum). Salus respublicae summa lex is a common legal dictum, 'the main law is [that of] the safety of the state'.
As for caput, Livy, for example, has capita coniurationis for 'the main conspirators' [Liv. 10, 1 capitaque coniurationis eius quaestione ab consulibus ex senatus consulto habita virgis caesi ac securi percussi]. The phrase caput itinerum occurs in various itineraries, for instance Augusta Vindelicorum veluti Caput itinerum in itinerario Antonini. Caput litterarum and caput rerum also occur. The usage is easily adapted to other situations, e.g. caput aedificiorum, the main building.
There were some good suggestions in the comments, and I want to record them here to give them more visibility. If anyone wants to elaborate on any of them, feel free to add a separate answer. I made this answer community wiki so that I get no reputation (I didn't do anything!) and anyone can edit easily.
Here are some possible translations for "main":
- the prefix archi-