Between those HD 4890 is the fastest choice, but go with 5770 because the difference isn't much;furthermore, 5770 supports newer techs(such as DX11),runs cooler,quieter and also has less power consumption.
And yes if you get a DX11 card(which only 5770 is DX11 from your list),you can play DX11 titles.
Instead of searching for GTS 250 you may search for the GTX 460 fermi it's priced slightly above the 250.The 460 is faster latest in tech and DX 11 ready.
But at present u will see no performance difference on games between DX(10/10.1 and 11) labeled cards regarding directX.
Can't tell about the 4890 but if you have like a 450W PSU in your system then it will run the other two cards just fine.And about ram its better if you keep minimum 4GB(having shared 1GB with graphics and 3GB for system).