I don't have it in mind to run more then one monitor, but one monitor at full HD running in 3D is a goal.
If your goal is 3D gaming, then definitely go with an Nvidia card. The 6950/70's are limited by AMD's 3D support, which includes a max resolution of 720p and you have to use 3rd party software.
Of your options, the 580 is by far the better choice for your goal. However, I'd recommend two 560ti's for about the same cost and much higher performance in most cases.
I have been able to compare both Nvidia and AMD in 3D, and Nvidia has a much better offer.
A couple of these would be my choice (or comparable offer): http://www.newegg.com/Product/Product.aspx?Item=N82E16814130604