I just put together a new budget system a month ago. It's only a temp computer for photo editing and will be the Home Theatre PC - HTPC in a few months as I need one anyway and will be willing to go bigger/better for a work system.
If you want to strip XP down use nLite, it's a great free program.
The system I'm running XP and LR on now cost a total of $302 CDN taxes and shipping included.
AMD Athlon II X2 240 Dual Core Processor Socket AM3 2.8GHZ - $65
MSI 785GM-E65 785G mATX AM3 DDR3 - $79.99
Seagate Barracuda 7200.12 500GB SATA2 3.5IN 8.5MS 7200RPM 16MB $54.29
G.SKILL F3-10600CL8D-2GBHK PC3-10600 2GB 2X1GB DDR3-1333 CL8-8-8-21 - $49.99
I'm using the onboard ATI 4200HD graphics card with no issue. LR does slow down a little when I'm editing up to 800+ photos loaded at once. By slowing down I mean less than 1/2-1sec before changes show. For the most part it's near real time. With less images it's a dream to use. Exporting/Rendering 830 photos took about 5min vs. 1hr per 150 photos on my old Athlon 1.2Ghz.
Dual core is a must and both are definitely used. I read LR doesn't utilize 4 cores for most work anyway but I will be getting one for the next built just to make the system run that much smoother and allow head room if work is to be shared to the other 2 cores. I usually have the TV running through a tuner card on the computer while I'm working also.
Unfortunately this computer is on the net right now so by rights I will have a 3rd system for every day use and the other for photo editing. Before that happens I'm eyeing a few 24-26" e-IPS monitors; I'm embarrassed to say but I'm still using a 15"(14" viewable CRT).