Have you read Help:Cite?
It doesn't tell me what type of citations to use (ex. MLA, APA, Chicago, etc). Am I allowed to choose what type or is there a certain way?
There's no standard there. You are definitely allowed to pick. Or come up with something that suits your wiki better.
I don't know what your wiki is about, but for example, with TV series, most wikis simply link to the episode. For books, the chapter. Some wikis go all out by also crediting the author in the link, whilst others don't even bother with refs (boo on them). Do what works for your wiki.