React uses MIT.
Graphcool framework uses Apache 2.0.
AFAIK (and I'm not a lawyer) neither of these licenses care how you then use libraries licensed by them. So, if you want to make your own package MIT, that's fine.
If you're using GPL licensed libraries, then GPL has requirements about releasing your code under a "compatible license".
It's worth reading around this subject, but if your intent is to make your code available to people, and you don't care how they use it or distribute their code, then MIT or Apache 2.0 are worth looking at.