No, it doesn't have to be castle-themed. I sometimes use a modern themed guy:
instead of this guy
(it's really the same guy in different clothes).
As to choosing one, just pick some fig you really like. Some people mix and match pieces to try and get a fig that looks like them, some use a character from their LEGO world, some just use a fig from their favorite theme. Some people don't go with a fig at all, but instead use an animal or something (e.g. Troy's dragon or Pat's monkey).
Sometimes people change up their sig fig for fun, like for instance I've got variants for different holidays, like these for Halloween and Christmas:
Or you don't have to have a fig at all for an avatar. Some people use things like shields or whatever.
Basically there's no rules - go with something you like and have fun.