I raise when I have no money left , I have enough political capital and speeches don't look like a good option where I stand (or in an important state). I pick my state at that time (when I've still got enough money to go there). I pick the state by order of money they can give. Since they give more money when I have high awareness, I make sure that the first HQ's I build are California/Texas/NY and other rich states. That ensures I'll get more money there if it's early game.
Don't know about likely % vote. It looked like it had an impact in one of my games, but it may have been low awareness to begin with.
I never build bigger HQs, so I can't say about these.