Choosing a line?

[thatpfunk]

The game is $2-4 NL at Sycuan casino in San Diego. It is a great game but most of the really bad players are shortstacked w/ around $150

Hero~$800
Villian~$900
Limp-a-long ~$175 (he is very bad and will call with any draw, piece of the board, or overcards)

Villian is one of the few thinking players at the table and attempts to play well. He is relatively inexperienced however and can be very aggro.

Hero is BB with A [img]/images/graemlins/diamond.gif[/img] A [img]/images/graemlins/heart.gif[/img]

Villian is Utg+1 raises to $14, 2 callers, Hero raises $45. Villian calls, 1 limper calls, other drops.

Flop: A [img]/images/graemlins/spade.gif[/img] Q [img]/images/graemlins/spade.gif[/img] 4 [img]/images/graemlins/heart.gif[/img]

Hero checks, Villian bets $75, limp-a-long calls (he has only about $50 left).

What is the best line from here?

How much better is betting out vs. check-calling vs. check raising?

What changes if the turn is J [img]/images/graemlins/spade.gif[/img], X [img]/images/graemlins/spade.gif[/img], Jo, or complete rag?

Thanks