Go for an AMD. I've got nothing against Intel(well, not too muah anyway) as i'm writing this on a dual PIII 650 as well. 1gig ram, all SCSI system. Home computer is dual celeron 400 512mb ram, all SCSI. Sure they work fine, and if you want 2+ processors go with intel, but for home/budget use, go for AMD.
The compatability problems occur with low quality boards, low quality memory (both of which Intel also suffers from), and low quality power supplies (do to large power draw). Most of the compatability problems you may have heard about are from back in the k5 and k6 era. AMD is cheaper and just as stable as intel machines with the same quality of parts. The more processor power the better, and with a PIII 1ghz going for 439USD, you can save 100USD and get a 1.1ghz AMD Thunderbird(337USD). If you want to go cheaper, you could get an AMD Duron. There is no reason to get a celeron nowadays unless your going for inexpensive notebooks. The Duron performs around 10% less than a comparable PIII or Thunderbird, yet costs much less. An 800mhz PIII goes for 179USD, Thunderbird goes for 127USD and the Duron foes for 93USD. Not too shabby.
A nice Abit KT7 (with or without RAID) isn't too expensive (122USD w/o RAID, 138USD) and is remarkably stable.
with the current price of memory, you'd be crazy not to get 256+ megs (if you build it yourself). 256mb PC133 SDRAM goes for 101USD, so even 512 isn't out of the question...
120USD for a 40 gig harddrive and you'll be all set. If you want a 7200 RPM drive, 156USD for that 40 gig... Still not bad at all.
Sound cards would be whatever you choose, same with video car. If you want this for sound pimpin, i'd suggest staying with whatever is cheapest that has drivers built into windows. Many problems with any computer is traced back to non-micrsoft certified drivers. If you want to play games, i'd suggest an ATI Radeon video card, just because it's relatively cheap (131USD w/o TV I/O). If you want more power than that, a GeForce 2GTS(161USD) or GeForce 2 Ultra(429USD)...
Use whatever mouse or keyboard you are comfortable with. I'd suggest skipping over the ultra cheap keyboardsand mice, as you are in direct contact with these and a cheap mouse is really annoying after a while...
Any cheap modem will do if your stuck on a dial-up connection to the net. If you plan on alot of online gaming, i'd suggest finding an ISA 56k modem or external model. These will outperform (and cost more) than the typical 20USD cheepie modem.
Network cards I woul suggest getting either Netgear, Linksys, 3Com or Intel. All will work reliably and have large followings. Prices range from 20USD to 60USD for the standard network cards.
Monitor, i'd say go for a 19" model. Some people insist on getting expensive monitors, and while they may look slightly better, getting a larger size is more important if you have alot of windows open at once. Acceptable 19" monitors can be found for 213USD.
These are just my suggestions. I'd be happy to debate this with anyone in a friendly manner, as i'm not into flaming people with differing opinions...
-=Whittey=-