How much of your old pc can you use, like hard drive, case, psu, etc?
FX 6300/ 7770/7790 fall in to that bracket, and game reasonably well.
Look up the Tom's recommended builds for different price brackets to give you a good idea of what you can do on that budget.
If you can re-use any parts, that will help a lot.
Let us know if you need to get everything, including monitor and OS. That will limit you a lot more.