$500 is enough for a gaming PC nowadays, however I'm best at building PC's, so I can't recommend a branded PC.
Make sure to get a computer that has:
A CPU with a decent cache size, however L3 cache is not important.
A CPU that has at least two physical cores, more than two isn't necessary.
A GPU that is ATI 4000/5000 series, or Nvidia 200 series for that budget. (Or better if you can
)
At least 3 or 4 GB's of RAM.