I think this hand would have been easier to play if you had exercised some pot control. Indeed, it is a good idea to raise with limpers in the hand when you are OOP, but that really isn't the situation here. There were only two other players in the hand when it came your turn to act in the BB: MP1, who min-raised, and the BTN, who called the min-raise. Your raise to 600 was 6x the previous bet, or 12 BBs. When you did this, you risked folding out both of the other players in the hand, and created a large pot which would be more difficult to maneuver in post-flop. A 3x raise to 300 would have been more appropriate here.
I think your c-bet of a little over half pot is good here. This flop is pretty dry, you are almost certainly ahead with AA, and a lot of worse hands will pay half pot to see another card.
Your turn bet of slightly under half pot is also fine. A little over one third of your starting stack is now committed though, and it definitely would have been better if you hadn't raised so much pre-flop. When MP1 smooth calls your turn bet, you have to figure that he has something like AQ, KQ, a big pocket pair, or maybe even a set. It's also possible he's foolishly chasing the flush draw. Two pair is pretty unlikely here. What two pair combo on this board would call your large pre-flop raise?
The 6 on the river is pretty much a brick unless he was chasing the flush draw with 7h8h. You have to figure that AA is still probably the best hand here. With these stack sizes, rather than shove the river, I would have bet about 1800 (one third pot). This is usually a better way to get value from hands such as AQ, KQ, JJ, and TT. Given the pre-flop and post-flop action, he has to be concerned that you have an overpair or a set, and I'm not sure he calls a river shove with a worse hand except perhaps KK. If you thought that by shoving, however, MP1 would put you on a steal and call off most of his remaining stack, then it was well played sir.