Users will need more info before leading off it to offer advice. I can say you won't get a lot with that budget as far as a 'gaming system' per se, goes. It will be hard to find anything with dedicated graphics below $700 - $750.
You might want to consider an A8 or A10 (AMD) system. Their integrated graphics is a bit better than the Intel HD graphics, just not as good as having a discrete/dedicated GPU.