I'd rather buy a laptop then a computer which would take a lot of space in your room. Never been a fan of desktops.
A laptop with good gaming specs would be AT LEAST $2000. Actually come to think of it, I don't even know how you'd be able to get 2GB of GPU power on a laptop. One could settle for less of course, but you won't enjoy Bioshock Infinite, BattleField 4, Crysis 3, Rome II (or for any other game in the future) at the same level. Its exhilarating to have 0 frame rate issues on ultra high settings (With mods added and all !)