As a baby, you can hear all phonemes. As an adult, many phonemes are experienced as one sound, even if they are different. Often ordinary people can’t re-learn the difference until after years of listening to fluent speakers- such as the aspirate consonants of Hindi or the double consonants of Swedish. Conlangers that wish to attract fans should ignore these facts at their peril.
Everything and the kitchen sink. Dritok, Ithkuil, gjâ-zym-byn fall into this category. These languages have radically different phonetic structures, so chipmunks can speak it, so you can do some sort of information compression and so it won’t be mistaken for an auxlang. I don’t think anyone expects these to be spoken, except as a sentence or two as a party trick. Even the designer of Ithkuil has reconsidered the phonetic inventory in favor of fans and way from a large phoneme set, by designing Ilaksh.
Same Phonetic Inventory as X. For Esperanto, the inventory is much the same as Bialystok Polish. Na’vi is much the same as English except for a handful of exotic sounds. The advantage here is that it is relatively easy to find materials to listen to to learn the phonetics of those languages and then apply it to a conlang.
This is somewhat out of style because conlangs that ape natural languages too closely are considered uncreative derivatives. But it’s also a practical choice. It should be learnable by at least one existing language community and the extra sounds is a minor burden and possible not important should fans fail to ever get the extra sounds right. It would be like listening to English with a Japanese accent. Sometimes the l->r transform causes problems, more often not.
Ordinary, but Extra Exotics. This would describe Klingon, whose alphabet isn’t especially large, but has a bunch of harsh noises. Klingon is also noted for having unusual distribution of phonemes. I’ve read posts where people harp on if a distribution is natural or not (such a language lacking certain categories of sounds), but for language learning, I’d pay more attention to crowding. The more similar sounds you have, the more phonetic misery you will be inflecting on the fans of your language.
Radical subset. This is a common auxlang feature because it makes the language pronounceable for the most people. Toki pona is a good example of this sort.
A conlang doesn’t have to be an auxlang. If it isn’t an auxlang, it doesn’t have to be over the top difficult with the phonetics. The odds of anyone learning to read and wrote a new conlang are slim, the odds of getting two people to speak it are slimmer. The odds of getting two highly trained and talented phonetics experts to follow your phonetic recipe are getting to be infinitesimal.
By the time you have 12 uncommon sounds in your language, you might as well specify that is only be spoken by rhythmic contractions of the sphincter muscles whilst farting.