Since I make a new character for just about every RP, I tend to go with a few personality traits to start. Very basic things to give my character a direction I want to go in, which I can then develop as I RP the character.

A few from recent RPs:
->Argumentative, Challenging, Charismatic, Proud, Compassionate
->Compassionate, Stubborn, Restless, Courageous
->A touch standoffish; can be charming when she wants to; kind - but only when no one can see her being so; sometimes does things 'for the hell of it'

So I have a general idea of how I want to play a character, then branch out from there as I rp.