I rushed through the beginning of the game, choosing Oshawott due to the fact that it is the same type as the first Pokemon I can obtain. I beat the first gym, and then caught Froggy, the typole, right before the second gym. After a lot of training, he was able to solo the next gym. BarrelRoll was caught soon after that, and I proceeded to destroy the next three gyms. I believe I can catch my next guy here, so I'll stop for now.
Froggy the Hasty Seismitoad (F)
Level 38 (Swift Swim)
BarrelRoll the Hardy Scolipede (F)
Level 33 (Swarm)