It looks like you're considering buying a computer from a pre-built company. Don't. It is very easy to assemble your computer yourself, assuming you can read an instruction manual. This will save you hundreds of dollars and/or get you a far better computer than you would have gotten from a pre-built company.
Assuming you already have a monitor you're happy with (budget ~$100-400 for a cheap to top end 1920x1080 monitor otherwise) consider the following build:
This is a one-time use license for the computer you build. Always get the 64-bit version.
CPU: i5-3570k ($228)
This is the best CPU for gaming if you want to moderately overclock your processor (added performance). A non-overclocking selection for CPU/Heatsink/Mobo is in the spoiler selection below if that sounds too scary for you.
CPU Cooler: HR-02 Macho ($53)
A good performer and one of the quietest cooling fans you can find. Note that it is much easier to install with a very long-necked screwdriver (18ish centimeters).
Motherboard: MSI z77-g43 board ($119)
Motherboards are all based on the same intel chipsets (in this case the z77), so there's no reason to buy a more expensive one unless you want to do something fancy like overclock super high or get 2 video cards. This one is one of the best 'cheap' mobos because it has 3 4-pin controllable fan headers, while many only have one.
Non-overclocking selections ($298 vs $400)
Warning: Spoiler! (Click to show)
GPU: 7850 ($250)
Strong enough to play the games you mentioned at maximum quality at any resolution, will play even the hardest to run games smoothly at reasonably high, though not maxed, settings for a 1920x1080 resolution.
Possible upgrade affordable if not overclocking or you don't need windows
Warning: Spoiler! (Click to show)
RAM: 2x4GB 1600mhz ($43)
Case: Antec p-280 ($100)
Case is largely a personal choice. This one is built to be relatively quiet, and is also large. It has a large top-mounted fan which some people don't like. Some of the better options for a cheaper case (from the same website) would be the Bit Fenix Shinobi or the Coolermaster HAF 912.
PSU: XFX core 450w ($40-$10 rebate)
Great deal on a quality power supply in the right wattage range. Yes, some online calculators say you'll need more wattage, but they're built to take account of the many terrible PSUs that lie about the power they can provide.
HDD: WD Caviar Blue 1TB ($90)
If for some bizarre reason you want even more space, you can get a 2TB drive for $20 more.
SSD: Crucial m4 128gb ($125)
SSDs are super-fast hard drives that make computing much more luxurious. Not necessary for gaming, but useful for MMOs because they reduce the time it takes to load graphics textures on the fly (which should reduce ironforge lag & make PvP targets just entering into view appear a split-second faster, etc). Otherwise reduces loading times for accessing data on the SSD. Put your OS & most-used programs on here, using the HDD for general data storage & media files.
SATA cable ($3) (mobo comes with 2, you have an SSD, an HDD, & a DVD-burner)
Overall, this is a far, far better computer than you can get from a pre-made. Everything from a better CPU to a better case to a better GPU to an SSD. You could go cheaper if you wanted as well, these is a pretty nice component list overall. Case could drop $50 for a less swanky case, the SSD can be removed, the HDD could be halved in size for $20, etc., etc. If you have $1200 though, the above should be just about perfect for a gamer.
Total Tower Cost (no mouse/keyboard/speakers/headphones/montior - Windows IS included in the price):
Recommended overclocking parts w/7850: $1148
Recommended overclocking parts w/670: $1298
Recommended non-overclocking parts w/670: $1196
Recommended non-overclocking parts w/7850: $1046
P.S. If you don't have a gaming mouse I highly recommend one. I love my Mionix Naos 3200, which is amazingly comfortable for a right-hander. Perfect ergonomics, in my opinion. Although hard-core MMO players might prefer something with a lot of macro buttons, like a Razer Naga.