Re: $600 AXT Gaming computer
I recommend not using ebay for building a computer. A website like Newegg, Microcenter, or even amazon is usually a better alternative.
Also, that CPU and motherboard you listed are already sold.
It all seems compatible, but what about a optical drive, or Windows. Also, that power supply is likely of low quality. I would opt for a Corsair, or Antec, 500w-600w will be plenty, that 750W will go to waste if it even can supply nearly that much wattage.
Build to be updated, a reminder to myself.