Ya question is akin to asking what size engine ya need in ya truck when ya haven't told us how big ya truck is or what it's expected to pull. If we talking 1920 x 1080, DX11 and hi settings, the 5770 just doesn't cut it. At ATI, you'll want at least the 58xx series.
It's perty good battle right now between the 6850 and the nVidia 460.
This superclocked version retails for $10 more than the card you listed but has a $20 rebate and $15 promo code, for a net cost to you of $190