Wild Battles are handled on your own. You have the creative freedom to handle that however you want, within reason of canon. No roflstomping tie-dye ratattas on the tallest peaks to evolve Arceus. If you look at the rules, you'll see some rules regarding leveling and wild Pokemon. Pokemon start at up to level 20 when caught from the wild I believe.
You may find the evolved form(s) of a pokemon if that pokemon evolves before or at level 20, in addition.
......Honestly, I'm still, probably, going to have a billion questions about this fantastic RP. Hahaha. Sorry. --How are wild Pokemon encounters handled? As soon as Wyatt's class is over (whenabouts should I say he leaves class?), I'll probably scoot over to the sea or the forest.