Best computer: One you build yourself
Best retail gaming computer: Cyberpowerpc.com
As most people have told you, building your own is the best way to go. You can tailor the parts to your needs and not get anything you don't need. Building nowadays is very easy, I suggest the DIY videos on Newegg's website, I will put it in my sources. It helped me with my first build, everything from putting it together to installing the OS to updating the drivers. Now I build comps for all of my friends and family and love it.
However, building computers isn't for everyone, and retail computers tailored towards gaming aren't easy to find as high-end pre-built machines tend to be CPU-Heavy without sufficient graphics.
ALIENWARE IS NOT A GOOD GAMING PC TO BUY. Do not listen to anyone who says otherwise, they pay $500-$1000 extra to have a spaceship looking case. If you want performance... in quality, known cases like Cooler Master or Antec at almost the cost of what it would be to build it yourself, go to Cyberpowerpc.com. There is no comparison at the price they sell things, I think their profit margin must be almost entirely bulk discount from manufacturers, because I price out individual parts and sometimes come in over their prices.
They can also be customized with anything you want, their library of parts seems to include most of the best parts from Newegg. They have one of the best warranties in the business at 3 years, and excellent, knowledgeable customer service. If i didn't love building computers myself so much, I would buy from there exclusively.
I would look for a computer with the i5-3570k, a GTX 660ti, and 8GB 1600Mhz RAM