It's worth mentioning that the power supply I included was garbage so as not to affect the budget too much. Also an extra $25 gets you 16GB of RAM if you shop around.
If you want to make that computer better, I suggest you spend the extra $25 for the 16GB of RAM, move up to a better power supply, and maybe consider a less hideous (and less affordable) case. These changes would bump you into the $750-800 range. Not necessary by any means.
Power supply wise in the cheap-er range I like the Seasonic SSR G series, the EVGA B2 (not to be confused with B), Superflower HX.... there are many more. EVGA W and B powersupplies are about as low end as you can get without owning a fire hazard/power surge fail guarantee box (IMO)