Arcade game main board replacment

What im looking to do is replace the whole thing with an arduino, It has 3 motors to to control one to move the carousel left when the button is pressed one to move the arm up when the button is pressed. there is a small ir beam to sense when the game has paid a win

My guess is that a Mega2560 is a better Arduino as it has more SRAM, 4x that of UNO. Unless you are experienced in game design, this is likely to be a frustrating project.

Ray