Pokemon Neo Challenges

Yo. I'm Kaizen, uhm....first of all I guess I'll say a few things about myself. I've been a pokemon fan for years, and have enjoyed not only playing the games but also watching the show. My favorite character in any of the pokemon games/show is without a doubt Volkner, followed closely by Cynthia. As such I'd like to post the pokemon that I'd like for my starting team, I'm kinda new and although I've read the rules, I don't quite understand whether you choose 3 at the same time or whether you chose one and then fight the others to try to catch them. If someone could please clear that up I'd be extremely grateful.

My hopeful team (in order of preference just in case) is:
Milotic
Gible
Eevee

I would also like to schedule a battle with a moderator for my dorm if at all possible.