Okay so AU in which The Doctor wasn't the one who escaped the Time War.

In this AU, the Time Lord who escaped was the equivalent of a monk. His name was The Brother. His regenerations always tend to be young men, late teens to early twenties in age. The reason for this is because, as a monk, he has the ability to hone in on his regenerations, and control them slightly. He sticks with the younger ones because it means he's less likely to have to regenerate due to old age.

I would play the brother.

The companion could be male or female (this is an AU after all.)