I have quite the experience on computers, and there're several computers you should stay away from:: Dell- Dell has a lot of back light problems, slow, and not built for gaming needs. HP- HP's tend to literally fall apart, also not gamer friendly. Now with that said there're plenty of others that are completely useless as well I wont go any further.
Cheap gaming PC's
Now gateways usually run a bit slow, there considered Medium End computers, they do how 'ever possess the capacity to play games efficiently. Toshiba Medium to High End, You can get these with 1Tb HD 8Gb ram also Radeon HD Graphics <Medium End graphics. good gaming PC. Samsung, medium-High End there a bit more expensive, If what you are looking for is the NVidia GeForce Intel Core i7 these are going to run about $800 -$1,000 great starter computer for gaming.