If you're not looking in building your own PC, then I want to ask you this, do you know how to install a video card? The reason I ask is because I would suggest you get a prebuilt PC and buy a video card on the side and install it yourself.
For prebuilt PC, I'm not sure which is your favor brand, but I got a couple of prebuilt PC from dell a few years ago and I think their service was pretty good. You can go to dell.com and chat with their representative and tell them what you want.
Here's something you can keep in mind:
CPU/Processor: with 1~1.3k budget, you should go for AMD, Athlon II x4 640 is cheaper, and you can play your game at mid to high range (depends on your video card). Or Phenom II x4 945 (since you don't overclock, you don't need to get 955 or 965, this one is better than Athlon II x4 640, but more expensive. You can compare the price between the two before making your decision. With this cpu, you can run the game at high setting, again, that also depends on your video card.)
Memory/RAM: 4GB is good enough for you, no need to get anything more than 8GB.
Operating System: Windows 7 64bits. If you get 4GB or more ram, you have to use win7 64 bits in order for the system to recognize all the rams.
You would also want to pick a power supply with 500W (if you're building the pc from dell, I don't think they let you change power supply setting, so you may want to ask their rep directly about this.)
When you're picking your computer online, they will ask you to pick a video card, you can just pick an intergrated video card because you're buying another card somewhere else. (again, I'm not sure if you can do this directly on the site, need to talk to their rep)
After you pick all the parts you want, find out how much it's gonna cost, and whatever money left would go to the video card. For video card, since you have an AMD cpu, I would suggest you to go with an AMD card as well. You can get a card from www.newegg.com. Depending on your budget, you can get a HD5770, HD6850, HD6870 or even HD5870 (the price for 5870 is only a little bit more than 6870).
I'm sorry if it sounds confusing, but I don't usually buy prebuilt pc, so I'm not sure how fexible they are in terms of picking the parts.