budget is $250, and screen resolution is 1920x1080
If you are looking at the absolute minimum that can play diablo III at highest setting, the 6770 it is. http://www.tomshardware.com/reviews/diablo-iii-performance-benchmark,3195-5.html
But since you are upgrading & have the budget anyway, it will be good to go for a more powerful card. While Diablo III is not very demanding games, others might be.
Here is a good one at $220 after mail-in rebate:http://www.newegg.com/Product/Product.aspx?Item=N82E16814161406