I want to help! (based off my experience, please feel free to politely correct me if anything I say seems wrong)
1. Try to stay away from Alienware stuff. My friend bought one for well over $1200, and I built a very similar system for around $800. (using some lesser brand RAM though)
2. Graphics card is very important. Don't misunderstand, a good CPU is important too, especially for games that use the CPU more, but overall, a graphics card is something you DO NOT want to go cheap on. That i7 or AMD 8350 can only go so far on its own.
3. Also don't go cheap on a power supply. If you don't plan on building the computer yourself, rest assured that most prebuilt machines will already contain a very decent quality PSU. However, if you do build it yourself, whether now or later on, a cheap power supply could potentially ruin your day. I've made that mistake at least twice, with power supplies dying, and even destroying my GTX 480 a few years ago.
4. Compatibility is very important. Not just any CPU can go into any motherboard. Some people would consider this to be PC building fundamentals, but when I first started building, I made this mistake and wasted a bit of money I didn't need to. An AMD CPU won't fit into an Intel motherboard, and vice versa. Simply check the socket of the CPU you want first, for example, an AMD with AM3+ will only go into a motherboard with a AM3+ socket on it.
5. You will not always need to keep 100% current with your computer in order to get a great gaming experience. I hate people who misunderstand this. I had one friend completely convinced that you needed to spend at least $600 on a new graphics card every year. This is completely wrong. If you buy a high end, or even mid range card to begin with, you'll potentially won't need to upgrade for a couple years. If I still had my GTX 480, it would STILL be able to play games today at probably their max settings, though not guranteed 60FPS.
That's all I can really think of off the top of my head...it's family time today, so I can't sit here forever thinking of this stuff. The rest if pretty much just stuff you can Google, and then just play giant Legos putting everything in. I'm sure everyone else here could help you more than I can right now.