Need help choosing a gpu $160 budget

i plan on using this card for casual gaming like farcry 3 and battlefield 3 i would prefer to play on ultra at 1080p on single monitor.

i am looking to buy this within the next 2 weeks or maybe 1 week

i am willing to use any website for the card preferably ebay





these are the specs to the setup i will be applying it too

processor
AMD FX-6300 Piledriver (Vishera) 3.5GHz (Six Core) 32nm, AM3+ 8MB Cache

Motherboard
MSI 970A-G46 AM3+, AMD 970, SLI & Cross Fire, SATA3, USB 3.0, GB LAN

DDR3 Dual Channel memory:
8GB (2x4GB) PC12800 DDR3 1600 Dual Channel

Case
Apevia X-plorer 2 Black, front USB, eSATA, LCD temp. display

Power Supply
Thermaltake TR2 600W ultra quiet ATX Power Supply, SLI & X-fire ready


monitor: dell ips 1080p model=s244ol
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current cards i am looking at are

gtx 295
radeon hd 6950
radeon hd 5870


to my knowledge i dont care if its nvidia or ati

thanks for the help in advance