Regarding building your own or getting a company created...
I've done both. While it can be cheaper and more rewarding building your own computer, some components just don't work well together. I had a Gigabyte motherboard once that was SLI enabled. Though it never worked right. If I connected it to my TV, the graphics card would not send out a signal to both monitor and TV. I tried replacing the card via warranty, and same problem. I took it to a friend's who had a different mobo, and the card output the signal no problem. Clearly it was the Gigabyte mobo. Time and again i'd contact their tech support. I had the mobo replaced twice. The issue was never resolved, so I had to decide between spending another $249 or just dealing with it.
I've found that a prebuilt Dell/whatever plus a good graphics card and some more RAM is more than enough. One thing to consider is that typically large companies like Dell have components specifically built for them, so there's a better chance that they will work together. Plus if one component fails, I just have one place to call. That said, it's hard to spend $1000 on a pc and then more to upgrade its components.
If I were to buy a PC tomorrow, and plan on spending around $1k, it'd probably be something like this: http://www.amazon.com/Republic-Gamers-G55VW-DH71-15-6-Inch-Laptop/dp/B009AEW5HI/ref=sr_1_2?ie=UTF8&qid=1365360176&sr=8-2&keywords=asus+g55vw#productDetails
Throw in a good SSD, and you're done. I'm on a G73 right now and Battlefield 3 runs fine. Everything isn't maxed out, but I don't care - it's still far superior to the xbox. Plus I get the added portability of a laptop (mine is 17" and I think a 15" would be nicer for the portability, though I love the screen size of the 17"). An HDMI cable is all I need to hook up this beast to my AV receiver for 7.2 surround audio and my 1080p projector. xbox 360 usb controller takes care of gaming. USB or bluetooth mouse/keyboard also if needed.