I would definitely suggest the a10-5800k for a low budget build. They do mention buying a gpu later but with an a10-5800k and a new discrete gpu it would game circles around the cpu they have choses with or without the discrete gpu. But we still do not know exactly what all parts they need or the full budget to buy them with to give the best advise. If you could supply us with those answers and what parts you do not need we could recommend a few builds for you to get the best bang for your buck.