My first PC build, also it is a budget gaming rig.

A budget of $650? Sounds possible. As most games are GPU-heavy and not CPU-heavy, it should be possible to hit that kind of performance by getting a decent GPU into the build. Probably a Radeon 7870 or a GTX 660 would do the trick. However, since your budget is including a monitor, and I can't tell if you need an OS...

Now, I changed the case on ya- this way, you get a USB 3.0 port to take advantage of the USB 3.0 header on the mobo. You can switch back to the original case if you prefer, however, and save a little cash in doing so, but you may not have USB 3.0 ports to use.

If you don't need Windows 7 for whatever reason, that's another $91 you can put toward a video card, which would probably get you to a Radeon HD 7850 1GB card easily (maybe even a GTX 660 if you're lucky, especially if you went back to the original case you mentioned). It's just barely in your budget. It also doesn't include a keyboard or mouse, but you could probably get the one you mention in your list easily enough (or go to a local goodwill store and pick up some cheap ones until you can afford to get 'em later on).

It's an Intel build, not AMD, but it just might get you the performance you're looking for if you went with a Radeon HD 7850 or GTX 660. According to the Tom's Hardware Skyrim benchmarks here below, the GPU should get you High performance easily (and Ultra not quite so easily, but still playable at over 30fps)- http://www.tomshardware.com/reviews/radeon-hd-7770-7750...

That said, with the CPU being not even an i3, I wouldn't be surprised if there's a bottleneck in there somewhere. I'm not 100% certain about that. Still, the game should certainly be playable at Medium to High, though maybe not at Ultra.

http://pcpartpicker.com/p/lCxM