Honestly I started with the Fire type, that fire chimp. At lv 14 I knew he wuld evolve into this monkey that is 1/2 fighting. While fire has little/no effect on rock, fighting shatter them greatly so. The first gym is a rock type, so get to lv14 first.
In reality it is not mattering that much as you pick up plenty along the way. But as far as starting out, you'll have ground, air, and grass style which the fire one has the best chance against.