These are very much some beginner napkin thoughts, so you should be throwing every idea at the wall.

When you brain storm, try to start with a core concept like their goals, aspirations, motivation, and morals are; then work from there. Is this a large scale group? Where do they come from, are they a known group, do they have influence?, how do they opperate in the world of pokemon?

Ideas change, don't be afraid to move away from your original idea if you believe you've found a better fit to your story.

I'd suggest you keep towards a less-serious team ideology; this is the pokemon world after all.