Answering my own question because a followup seemed to be in order. Short answer is I used something from most of the answers given.
First, taking one of the suggested answers, I booted it off of a Puppy Linux live CD. I don't use linux every day, but it didn't take too long before I had the wireless network card working, and I even networked printing going using CUPS. Performance was excellent, at least compared to what it had been previously, so I was all set to turn this machine into my own personal Linux-based netbook (albeit a big, heavy one), and buy a new laptop for the kids.
However, my wife and I have been trying to do a better job of budgeting and saving money lately, and spending $400 or more on a new computer for the kids wasn't something we wanted to do right now. The kids would need a Windows-based computer for games and educational software, so I started to see what I could do back in XP. First, I used Revo Uninstaller to remove as much installed software as I could, particularly system tray apps that use up my already-limited RAM. This freed up enough disk space so that I could defragment the disk using Defraggler.
Things were running much faster now, but the 10 GB disk was still pretty much filled up. I ended up buying a new 80 GB hard drive on eBay for about $50 with shipping, which had the added benefit of being faster (5400 RPM vs. 4200 RPM for the old one). I replaced the hard drive, reinstalled XP, and carefully chose applications to install that were freeware and/or open source, and low resource usage whenever possible (lifehacker.com was a good resource for this). In particular, when installing apps, I tended to disable the options to "notify me when a new version is available," since these tend to be system tray apps that load at startup. The final list of installed apps looks something like this:
- Firefox + Adblock Plus
- OpenOffice.org
- Paint.NET
- Microsoft Security Essentials (antivirus)
- Adobe Flash
- Foxit Reader (PDF reader)
- Notepad++
- Defraggler
- TweakUI
- TreeSize
- DropBox
- KeePass
- Various kid games and software
This is now a very usable machine, both as a kid computer and for the occasional on-the-go laptop use, or when someone else is on the "main" computer in the house. With a $10 car power cord, it could play movies on long road trips, provided I rip the DVD on a different machine and copy the files to the laptop, as it has no DVD drive). I have to say that I have newfound respect for Windows XP: through three major service packs and hundreds of updates, it is still chugging along after 8+ years. I still may continue to play around with a linux distro on it, although I may try Xubuntu, as I wasn't crazy about the fact that you run as root in Puppy Linux.
1Hard drives are pretty cheap these days. An upgrade (even to say, 40 or 60 GB) would be in order if the motherboard would support it (which I hope it would - it might have a problem with stuff over 137 GB being so old, but hopefully under that should work fine). Also, if you go Linux, I recommend Puppy Linux for being small yet usable. – Nathaniel – 2009-12-15T00:35:12.313
If you have a copy of Windows 2000 laying around, give it a try. I have a 233MHz PC running W2K that works great for light web browsing – zildjohn01 – 2009-12-15T04:21:56.800