I'll disagree & suggest the 3gb 1060 or the RX 470 - whichever you can find cheapest.
If you're prepared to use the inbuilt shadow play or raptor recording/streaming features there's virtually no fps loss.
While there's no doubt that your CPU will limit both these cards & you're going to be sitting mid 40s the majority of the time fps wise my suggestion is for future proofing as much as anything else & also for the fact you'll be able to ramp up graphics settings to high easily.
460/470/1060
Current best priced 3 cards IMO.(if you're USA)
http://pcpartpicker.com/products/compare/pKX2FT,JMVBD3,RvjWGX/
Yes the 470 is $72 more than the 460 but absolutely worth it.
Ever upgrade it'll carry over to a new system well & should be strong enough for the next 2 years.
If your board is fm2+ then that allows you the 880k in budget aswell.
http://pcpartpicker.com/product/94s8TW/amd-cpu-ad880kxbjcsbx