BF3's a pretty demanding game... you're not going to be maxing anything on BF3 with a $150 card, but then again, you probably already know this
to be honest I would get something like a radeon HD 7750. it would be hard to avoid a bottleneck with your athlon II for multiplayer at high resolutions, but you should be able to find a happy medium with this combination. everything should be pretty smooth on single player as long as you don't try to max settings. besides, the 7750's a low end enough card that has such little power consumption that I would feel comfortable sticking it in an HTPC in the future
as you can see here, it'll get you decent fps at medium settings
http://www.anandtech.com/bench/GPU12/458
also on the same chart is the 6850 or 6870. if you don't plan on the HTPC build in the future, they'll get you more raw performance
am waiting for haswell myself. though I took the plunge and went sandybridge