Ah, but this is easy. Pokemon.
I mean, to the considerations in the OP:
1: only as strong as the average human - means bugger all in the Pokemon world. Every one's an average human, it's the monsters that matter.
2: only take what I have - again, that's fine, just drop by a Mart or the local Pokemon Professor's place and ask for some Pokeballs.
Once you've got the Pokeballs (and hopefully a starter) it's all relatively simple, right? Beat critters to get stronger, beat Trainers for money, beat Gym Leaders for prestige. Hell, you could even get a job in a local Mart or Center or whatever to earn extra cash. Other than that, life on the road, your friendly trained battle monsters at your side? Sounds good to me.