[strike]I would bump your budget up to 120$. If you set the budget too low, you are doing yourself a disservice. Since the $ to performance actually starts to increase[Not good!]. if you increase your budget, you leave your options open for a 750 ti or a 270x. If oyu have to stick to that price the i would recommend a amd 7450.
[/strike]
Edit: Just looked at benchmarks for the apu, can't really pair a gpu for this situation. Sorry 🙁