If you're up for the task, building is fun and rewarding. Plus you will learn more about your computer that way. The other side is that you, or the person that built it, are on the hook if something goes wrong. You will get exactly what you want though, and will know exactly what went into the computer, unlike many companies such as HP/Compaq or Sony.
With someone like Dell, you can get a computer for about the same price, at least here in Canada (this may be different in the UK and Europe), but with a 3 to 4 year warranty. They also tend to include bundled software for cheaper than what you would pay on your own. This isn't a problem if you already have the software, unless you want to keep using your existing computer.
I built my own computer and continue to play with it and add new things or try something different. For my family though, I always recommend that they buy from Dell.
As for playing Doom 3, you might want to wait until it comes out before deciding what to buy. Rumours have it that it can bring current top of the line video cards to their knees, and there are new generations of video cards from both nVidia and ATI coming out soon.
If you do decide to build, fire away with the questions and we will do our best to help. Good luck!
goates