Hey, if your gaming on a single monitor, (1920x1200 or less resolution) I would say go with the GTX560 ti, it will slightly outperform the 6870 as the amount of memory will not make a difference at that resolution range.
However, I would say that you should consider buying from newegg.com if that is a possibility for you, you can get that same GPU for $244 after mail in rebate.
The 6950 is on par with the 560ti but the advantages that it has is that you may be able to unlock the extra shaders to make it basically a 6970 which is much better than the 560 ti and It also scales much better in crossfire than the 560ti in sli (90% vs 80%) so when you decide to upgrade the 6950s will be better than the 560tis
they are pretty much at the same level the 6950 is amds equivalent to the 560ti. generically the 560ti will preform slightly better in nvidia sponsored games and the 6950 better in radeon/amd sponsored games but there very close
on this chart the 560ti hawk is surrounded by 6950s so there really about the same but if you look and compare the 6950 cf to 560 ti sli the latter is greatly outperformed. Just make sure they both fit in your case and you have a strong enough power supply to power them.
Even 650w is overkill if you aren't going to SLI/Crossfire. A 500w from the brands I mentioned could easily handle what you are talking about with everything fully OCed.
FYI while RAM is cheap 16gb is still of questionable utility. Unless you know you will be doing something that uses tons of RAM(music production, rendering, HD video processing) I'd just stick with 8gb. Put the extra money towards something like an SSD for OS and apps if you want something that is actually useful.
ya you should be good w/ a 500w w/o sli or CF but if there's not a huge difference in price go for a 750-850w and you will be set for in case you decide to go SLI/CF in the future otherwise if you want to add another graphics card in the future you will need to buy a new power supply