At the $150 price point, the FX-8320. it's currently about $150 now and it's been as low as $130-$140 online and $100 at Microcenter. If you can't get the FX-8320 for $130, the FX-6300 for $110 is a good 2nd choice. I don't bother with FX-8350/6350 cpus as they are more expensive than the 6300/8320 and with a 970/990 board you can easily overclock the 8320/6300 with stock cooling to 8350/6350 speeds without much effort.
An i3 i admit would perform faster than the FX-6300/8320 at single and dual threaded apps, but newer games like Crysis 3 and Battlefield 4 like multi-core CPUs better. Since the next-gen console is an 8-core AMD chip, I'm guessing future games will benefit more from multi-core processors. So if I were building a new machine now, i wouldn't settle for anything less than FX-6300/8320 or i5/i7. Also, in terms of older games that only utilize single or dual threads, the FX-6300/8320 perform well enough that it doesn't really matter as with a good video card they provide acceptable FPS at 1920 x 1080 resolution.
In the $70 range, the G3220 or Celeron G1820 are good choices. Frys had the G1820 and G3220 for as low as $30. At that price point, you really can't ask for much more considering that a G3220 is faster than my e8400 OC at 4GHz.