I'm hoping to play games like Minecraft (max settings), Assassins Creed, many first person shooters (ARMA, Battlefield, etc.), Grand Theft Auto, and a handful of other games.
Ok, well arma, battlefield, gta are all really GPU intensive, and depending on what CPU and resolution you play at will depend on how good youll be able to run the game. All three of those cards will run the games at lower settings, at maybe a 1080p resolution. But if you list your actual budget, well be able to help you pick a better card for the money.