My philosophy in situations like these is to try to set things up so that any decision I have to make later on will be easier, often at the cost of the present decision being slightly tougher. What does that mean here? It means to try to keep the pot small when I have more chips to make mistakes with, and to try to get it all in when I'm low on chips.
On the flop:
With short effective stacks (effective = the smallest stack of the two of you) I'll want to get it all-in with AK and a flop with an A:
-- Out of position, I'll bet the pot on the flop. If called, I'll move in on any turn. If he hit his draw, sucks to be me. He clearly liked enough about that flop to call me, and chances are he's liking it with AQ or AJ.
-- In position, I'll bet the pot twice. I'm not quite as happy getting it all-in when I have position, since I want to keep that advantage. If I get re-raised at any point, I'll call or just push.
With big effective stacks, I want to avoid getting trapped. So:
-- Out of position, I bet half-to-2/3rds of the pot. If called, I'll check any turn and re-evaluate. To this particular turn, I'd call a pot sized bet and check the river. Few players will have the stomach to bet the river with anything weaker than a two pair hand since they must know that very few people fold. Therefore, I'll often fold to a large bet on the river if it comes to that.
-- In position, I'll pot the flop and bet/fold the turn with a half-pot-sized bet. If I get checkraised, I'm out of there against an unknown or typical opponent.