A GTX580 should be fine for you.

What does resolution have anything to do about graphics cards?

Sorry I just don't know.

A higher resolution (other settings variables) will require a stronger card. A 580 should max out your games at your resolution easy, and also at 1080.

Mmmmk.  Thanks for telling me.

And thanks to everyone else who responsed.

Now I just find out when prices will drop for the 580. ;p

Probably when Nvidia launch the 670 which if you are not using your GPU for compute (video encoding etc) will probably edge out a 580 in games. 

Is that "edge" worth another +$50?

IDK the card isn't out yet, it's due May 14 there will be reviews then. That should also coincide with better 28nm supply which should mean that there are more GTX680s available as well which hopefully will mean price drops on the GTX580 so it's worth waiting to see how the 670 mesures up anyway.

It's rumored to be ~20% slower than a 680 and be priced arround $400 in the USA so it might be cheaper and faster than a 580 in some games

Prices on 580's have already been dropping since the 680 released. I just picked up a pair of new GTX 580's at a really great price. ( two of these http://www.galaxytechus.com/usa/productview.aspx?id=165 )

I got them both for the price of 1 GTX 680 here in Japan!

If your getting to 580's why not just get a 590?

Isn't it like 2 580's in 1?

I have Core i7 3.03 quad from Jan 2011, 9GB ram, Win 7, ATI Radeon HD 6850 1GB GDDR5

I do the same thing with Skyrim, use tons of mods, and I've never had a drop in fps, I get a solid 40-50 easy, and I turn all settings to max, even 16x anisotropic filtering.  I also get a solid 50-60 fps in StarCraft 2 on the "Extreme" setting, even in 3v3 league matches.

So, I'd go with the 6850, and probably also bump up your CPU a little bit, but not too much, and you'll be fine.  Also, if you have room in your case, you could always try using one 6850 like me, and then if you need more horsepower a year or two from now, go Crossfire and add a second.  By then the 6850 will probably be around $100 or less.  It's about $135-$140 right now.

Best of luck, hope this was helpful.