I have come out of the closet to my oldest sibling and my cousin, no one else. I'm waiting until at least August to tell the rest of my family. I have a few other siblings. One of them won't believe me at first, I think, so I'm waiting to tell them. Will it hurt my siblings' feelings that I came out to other people before them? Should I tell them soon-ish so that they don't feel like I'm picking favorites or something?
It is entirely up to you who you tell, when and in what order. Tell who you are most comfortable with knowing, it's not up to you to spare their feelings.
I agree. This is an important moment for you, and it's important that you listen to your feelings and that you build up a comfort zone gradually, in the way that best fits your situation. If that means coming out to some people before some other people, then so it is.