I'm going to be getting my first phone for my birthday in October and I want to make sure its a good one that will last me a while. What I want is something that's powerful and has a long battery life so I can play Retroarch's DS core and Dolphin relatively with as little lag as possible for as long as possible without charging. I have no intention of getting an IOS device, so please only suggest phones that use Android! Good compatibility would also be nice so I can play all of my favorite games like BTD 5, Mage Gauntlet, Tetris, and Monument Valley. I'm not picky about size, as long as its smaller than a tablet. I have a budget of around $550. (I don't have to worry about the contract.)