byzrk

If I were you, I'd go with one of these 3 options:
 
If you don't mind a mining card, a used RX470, RX480, RX570, or RX580 would fit your budget nicely.  For around $100-120, you can buy a brand new RX570 that comes with 2 games.  Used GTX 970's go for around $80-100. You can find them at /r/hardwareswap, locally, or even on EVGA's website during Midweek Madness. These cards use a lot less power and thus generate less heat and would pair with your build nicely. Hope this helps and good luck with your upgrade.
 
 

Thanks for pointing me in the right direction. I've only looked as far as googling "fastest 1156 cpu" and found some $90 i7 880's and thought it wouldn't be financially worth it to upgrade to a faster CPU. I guess I should try exploring some more budget options that might be worth it for me.