For gaming, the graphics card is all important.
Spend your budget first there.
Here is a link to tom's best graphics cards for the money:
http://www.tomshardware.com/reviews/gaming-graphics-card-review,3107.html
Buy the best graphics card you feel comfortable paying for.
We tend to want to buy the most expensive multi core cpu, but for gaming, the cpu is usually not all that important. Most games will not use more than 2-3 cores, and the faster those cores are, the better. In the budget range, amd does decently. Past that, the intel cores are much more efficient per clock, so even a dual core i3-3220 with hyperthreading will be better than a fx-4300.
Read this article on best gaming cpu's for the money:
http://www.tomshardware.com/reviews/gaming-cpu-review-overclock,3106.html
Then decide on your cpu/gpu, keeping in mind an approximate 2 to 1 ratio of graphics to cpu budget.