i7 will offer you no advantage in gaming at this time. It is more adept at repetitive tasks like video compression, but gaming will see no difference at all between the i5 and i7.

Depending on how cheap you want, FX-6300 is probably your best bet, being decent performance on the cheap. FX-6300 is ~$110, cheap-ish mobo for $50-60, 8 gigs of whatever for $70, something like an r9 270x or cheaper old 7950 for less than $200, then cheap 1TB HD for ~$50, then case&PSU. A dirt-cheap CX-430 can power something like this if you're not overclocking.