You don't need a hexacore CPU, a quadcore will be fine if you're looking to game on a budget. I wish I had gotten in sooner, if I had I would've told you to go for the $600 mark and, with the money saved from going down to a quadcore, buy a better graphics card and perhaps a slightly more powerful PSU to support it, maybe 500w just to be safe. PSU's aren't my particular area of expertise, however.
I honestly doubt you'll be able to do much, if any, gaming on a GT 620 in this day and age.