For a budget, yet good performing processor, I would recommend an AMD Phenom X4 965 BE. With it's Black Edition designation you can overclock it beyond its stock 3.4 GHz AND it's only $75 at Tigerdirect.com right now. Of course, you'll need an aftermarket cooler. Something like the Cooler Master Hyper 212, which costs ~$25 at Amazon.
For really good performance, any of the 2nd or 3rd generation i5's will do (The i7 has hyperthreading, but games rarely use that). That i5-2500K/3570K are great for overclocking and cost $200 at Newegg.com (You can get $20 off from a V.me visa promo). However, if that is too much money, you can go for the i5-3470 ($180 on Amazon) or i5-2310 ($165 also on Amazon. The former will offer 1600 MHz RAM speed and better integrated graphics (but really, if you game, you should use a graphics card), etc. but costs $15 more.