The power supplies in pre-built, eBay type computers are the absolute cheapest to be found, that being one of the only ways to shave money of the build cost. It's seriously doubtfull that it actually puts out anywhere close to 500 watts, probably closer to 300 continuous watts. That said, it'd be a wise decision to replace that with one of better quality (easy to do considering) .
Since you do have the option to replace the psu, give some thought on the gpu, if buying one make it a match for the other, even if that means saving up a little longer. The end result will be better playability all round. I would start with the CPU, then save up and see if you can get a deal on gpu/psu, sin e now you won't be limited. A 6300 can handle any gpu currently made, so your options will be wide open instead of quite narrow.