I'm getting a 6850, which is almost the same as a 560 (which is better by just a minuscule amount, but if you want cheaper get the 6850, still plays many games on higher settings if not max). My friend enticeing on the IRC has the same exact build I'm getting, and he can run Skyrim on max at a smooth framerate with no stutters. A 6850, when combined with other good hardware, should even get you 100+ FPS in Minecraft. GREAT for recording.
If you have some more money to spare, a 6870 or even a 6950 (or 560 Ti or 570) would be even better. If you play a lot of WoW, an nVidia card may be better, just saying.
Also, I recommend Phenom II X4's for your processor, the one I got seems to be a great all-around gaming. Many will tell you to get an i5 2500K and overclock it, but I'm going to stick with AMD. Intel may be better in certain areas, but AMD has a better price/performance ratio (meaning you get more buff for less buck) and is just cheaper in general, and the build quality is still excellent.
AMD Phenom II X4 355 3.2GHz Black Edition (can be overclocked easily as it's an unlocked CPU)
8GB Kingston 1333MHz RAM
Radeon HD 6850 (can't remember the brand...I think it was either Sapphire, XFX or MSI)
I got the RAM and mobo in a bundle with the CPU, and the case I got came with a DVD burner and a PSU.
I can't use it till Christmas, it's just sitting in boxes in the dining room.