A GTX 660 would be the lowest I'd recommend if you want to play on Ultra. It's a great card for $230.
If you're sticking to BF3 then Nvidia is the way to go. BF3 just plays better on GTX's than Radeons. GTX 660 vs Radeon 7870 Features & PricingGTX 660 vs 7870 Benchmarks
You'll notice that the 7870 is faster in quite a few games but when it comes to BF3, Batman: Arkham City, Portal 2 & Starcraft 2 (not like SC2 stresses either card) the GTX 660 does win by a substantial amount.