Can't use a gun? It is a skill that can be learned unless there is a philosophical reason against them but, to each their own. I would enjoy using any gun I could find to defend myself or, if I had enough ammunition for target practice.
Anyway, I've spent my life trying to be a fairly good guy so I would continue to do so. I would do my best to disarm the bomb in Megaton so I would end up with a house.
At that point I would probably say, "The old man took off without telling me why so I hope he is happy. Maybe I'll run into him some day.". That would be about as far as that subject goes.
I might help with some of Moria's book but I sure wouldn't damage myself by breaking a leg or getting massive doses of radiation.
As one easy way to get money is to scavenge, that's what I would do. Of course this line of work has it's risks and anyone foolish enough to take a shot at me had better hit his mark with the first shot. It would be his last.
The very few raiders who have run away from me or the Enclave soldier who made no threats against me I would leave alone just as I did in the game.
After finding the mole rat converter I might take up mole rat hunting as another source of bottlecaps. Pretty easy living as long as the rat population holds out.
The fire ants could have their town and my only action there would be to take the kid out of there. He could stay at my house in Megaton until I got down to Rivet City where I would gladly send him to his aunt.
The kids at Little Lamplight probably wouldn't let me in so I would forget that place. Most of the kids there are brats so except for a place to sell stuff there's not many reasons to go there.
Slavers leave a bad taste in my mouth so I'm afraid they would have to go. No one has a right to own another person.
All in all, I think it would be an interesting life.