Push in on the flop or turn?

[AndrewRC]

Here's a hand I wasn't sure about...
Full Tilt Poker Game #1950734889: Table Corsaire (6 max) - $0.50/$1 - No Limit Hold'em - 0:56:17 ET - 2007/03/09
Seat 1: Luky Luk ($120.15)
Seat 2: R8R H8R 88 ($47.60)
Seat 3: Cephus Lives ($128.90)
Seat 4: kixaspokherGirl ($92.30)
Seat 5: Hayeater ($100)
Seat 6: AndrewRC ($130.15)
kixaspokherGirl posts the small blind of $0.50
Hayeater posts the big blind of $1
The button is in seat #3
*** HOLE CARDS ***
Dealt to AndrewRC [Ad Ah]
AndrewRC raises to $4
Luky Luk folds
R8R H8R 88 folds
Cephus Lives calls $4
kixaspokherGirl folds
Hayeater folds
*** FLOP *** [Ac Td Qd]
AndrewRC bets $5
Cephus Lives raises to $22
AndrewRC raises to $126.15, and is all in
Cephus Lives calls $102.90, and is all in
AndrewRC shows [Ad Ah]
Cephus Lives shows [Jh Kh]
Uncalled bet of $1.25 returned to AndrewRC
*** TURN *** [Ac Td Qd] [Qh]
*** RIVER *** [Ac Td Qd Qh] [8c]
AndrewRC shows a full house, Aces full of Queens
Cephus Lives shows a straight, Ace high
AndrewRC wins the pot ($256.30) with a full house, Aces full of Queens
Cephus Lives adds $100
*** SUMMARY ***
Total pot $259.30 | Rake $3
Board: [Ac Td Qd Qh 8c]
Seat 1: Luky Luk didn't bet (folded)
Seat 2: R8R H8R 88 didn't bet (folded)
Seat 3: Cephus Lives (button) showed [Jh Kh] and lost with a straight, Ace high
Seat 4: kixaspokherGirl (small blind) folded before the Flop
Seat 5: Hayeater (big blind) folded before the Flop
Seat 6: AndrewRC showed [Ad Ah] and won ($256.30) with a full house, Aces full of Queens

No way I can fold on the flop at this limit, however possibly just raising to $50 on the flop would have been a better play than moving all in. I gain value from hands such as AK or 2 pair, but if any face card comes on the turn, I could lose the action I'm trying to generate by not moving in on the flop. In this example, he'll obv raise me all in but what about in general? Raise to $50? Raise all in? or something else?