I guess my first is Intel or AMD...do you have a preference?
I put my system listed below together for $1500 including the monitor about six weeks ago. The system cost me about $1200 without the monitor and since then several of the component prices have dropped considerably (CPU, memmory, graphics card). Also, neither the SB Live Platinum 5.1 or the AIW Radeon are really neccessary...a 32BM Radeon and the SB Gamer or Phillips Acoustic Edge will do just as well with a savings of at least a hundred bucks.
I play UT quite a bit as well and it looks superb on my Radeon. A couple of my friends who owned GF2 ultras ditched their cards for Radeon 64's after seeing the image quality on my Radeon.
Edit: Oops...didn't realize you were only looking for a few components...heh heh.
Case: ANTEC SX830 - $81 shipped from Oniva.com - great case, good ventilation, easy access
Processor: AMD 1GHz w/ Chrome Orb - no more $225 combined from many places - with Orb you should be able to hit 1.2 on an O/C...other sink/fans may cool better but they're too loud IMO. You could save money by going with a Duron 650 and O/C to 950-1050...depending on your luck.
MB: Some like the KT7 Pro2A but I'm sticking with my KT7-Raid...take your pick.
Memmory: Go with 256MB of Muskin PC133 Rev 1.5 or 2.0, or maybe some Corsair. Mushkin Rev1.5 is running 133 cas2 (will do up to maybe 140-143 cas2) in my case rig right now...haven't had a single crash...not one. I say never skimp on memmory, 256MBon rev1.5 runs about $175 shipped but wait for mushkin specials: they do them all the time.
HD: IBM 75XP 45GB for about $150-170 - fastest IDE drive widely available on market
Graphics: Radeon 64MB DDR VIVO $240 at buy.com - you could get nVIDIA but why? Image quality is not as good...TV out is no good...and DVD playback doesn't hold a candle to the Radeon. The only thing nVIDIA has is a little more speed, but no GF2 you can get for $240 will out-pace Radeon by much...and "speed don't mean a thing if the image don't have that zing!" I know...that was corny.