If you are okay with a desktop, I think you could get a decent system for around $800. If you are willing to tolerate a Celeron processor, you could likely find a machine that just requires you add a better video card to be able to do the video thing.
But, I encourage you to think about the point you are at in life. I expect college will be coming soon. In all truth, a laptop that *won't* run all the games (mostly because of the video cards) may be a better bet for you, really. It will be much more invaluable in college. I got my first laptop in Law School, and it changed my notetaking and performance a lot. I was willing to take it to class and take notes on it. Rather than the numerous spiral-bound notebooks at the end of the semester, I just had to open my computer and -- viola -- I was able to easily summarize and synthesize the semester in preparation for finals (which are the *only* test you take in Law School courses, and which dictate 100% of your grade).
For a laptop to play games -- forget it. My Dell is marginal for graphics heavy games. With a 2.6Meg Centrino processor, a 126Mb Nvidia Card, and a 60GB HD, it ran me well over the $2K mark -- 8 mos. ago, of course.
The alienware's look like nice machines -- but I didn't go for one. It comes very "raw" and with a Dell I was able to get Word and other needed software, as well as a 3-yr. upgraded warranty with really good tech support. Another problem with the alienware's, in my mind, is that they come with a standard P4 processor, which is not really the best thing for a laptop. Yes, it runs games best, but cooling becomes a real issue.
You could always get a job to increase the money, and add to what your pop throws in.
