The 300 W AC Power Adapter, is what everybody else calls a 300 Watt Power Supply, the CPU or APU if you prefer takes a maximum of 65 Watts, so not a lot left for the other components. How would you feel about changing out the Power Supply and the Video card, would that blow the budget?
Something with and FX-4300 and an HD 7770 video card would be more suitable for gaming.