I'd say the absolute bare minimum for games to perform adequately would be a GTX 295. But of course you'd skip out on lots of features and a cheaper power bill. A 295 puts down a 460 really hard, but I'd say is the minimum for performance. As far as new cards go, I'd say a GTX 650Ti Boost or 750/750Ti.
Or an R7-260X or R7-265
All great budget card solutions