I hate to say it but there's not much worth recycling from the old system, at least in the long term. It's all old or "value" (slow) components.
You have a few options...
One is to try to fit an entire new system in under $600. I am pretty sure you won't be entirely happy though since you'd be stuck with "value" or old parts again.
You could get fast previous-generation parts. Go with something like an ABIT NF7-S motherboard and an AMD Athlon XP "barton" cpu, maybe a 2500+ or 2800+. A combo with those parts should run around $300. Add in 512 meg of PC3200 DDR sdram and you're up to $450. Toss in an ATI radeon 9700 (or GF4-4200 for a cheaper but still fairly capable older card) and recycle the rest, and you're still near $600.
Or you could start replacing components one at a time with some really good stuff. This is what I usually do myself, so my upgrades trickle in for just a few hundred bucks at a time. Start with one of the new AMD Athlon 64 cpus, maybe a 3000+, and an NForce3-250 motherboard. You'll need new memory, so get a single stick of 512 meg PC3200 or PC3700 DDR sdram. When you get more money, you can buy a second stick and take advantage of the dual channel memory controller. Reuse the rest of your system components as necessary, and replace when able. Don't get less than an ATI 9600/9700 video card, get an athlon 64 for the cpu, get at least an Audigy2 soundcard (I have a retail audigy2 ZS and it works fine), etc.
Oh yes... I finally made the switch from win98 to winXP home, and I've found that although I hated spending the money for what has been almost zero additional features I actually use, winXP home has been a bit more stable so I recommend going to winXP with your new rig no matter what hardware you end up getting.