If I was the average forum member here, I would simply say "build it yourself" or something to that effect... but since I'm not here's some lousy, non techie advice.
Of the three you mentioned, Dell gets the best reviews from mainstream users and magazines. They are rated highest for customer service, are very quiet, and generally well built. The biggest complaints I've read about a Dell would be component selection and upgrade options.
I haven't read too much about Compaq, but they tend to get mediocre reviews when it comes to construction & customer service. Some of their PC's are pretty cheap, though.
Alienware rigs tend to get strong reactions. I've read scores of glowing reviews; I've also read just about as many damning ones. Most complaints deal with limited customer service, instability (they like to overclock a bit) and/or bad parts. Alienware lets you pick from a good selection of components, but they are by far the most expensive of the three you listed. They are also notoriously loud due to the many fans they use.
Just under two weeks ago, I ordered a computer from Oxford PC. They are a much smaller operation than the three mentioned above but have a good selection of components, and better prices than Alienware. After checking Reseller Ratings, Anandtech Ratings, and the BBB Online I made my order. If things go well, the computer should ship early to mid week; I'll post a quick review here after I get it.
If money is your main concern, then maybe a Compaq, or better yet a Dell. If you want to get something that more closely meets your specifications, then maybe Alienware or perhaps
Oxford PC...