For gaming, you need a strong graphics card.
That will not usually be found in a pre built pc.
Can you build one yourself?
Here is a link to a $500 gaming build that will give you some ideas of what you might be facing.
The parts and prices will have changed, but the budget proportions are reasonable.http://www.tomshardware.com/reviews/gaming-pc-overclocking-pc-building,3273.html