Allyson:
Based on the information you've given us, it looks like you've probably got the iMac 600 or 700 - the fastest, most recent graphite iMacs (earlier ones actually had the DVD-ROM instead of the CD-RW). These were released in early or summer 2001, depending on the exact make, so the computer is technically a bit less than 5 years old.
Still, based on the specs, I really think you can run Tiger fine. The iMac is much like my poor iBook that just died, which loved Tiger. So here's what I'd recommend, if you really don't want to upgrade instead.
1) Up the RAM. It looks like it can handle up to a GB, and I'd suggest putting at least 768 MB in there. This will be, by far, the best, most significant hardware upgrade for that computer. (You can find out how much you have now by going into the Apple Menu and selecting "About this Mac" - if you have at least 512 MB, this step is not a necessity, but if you have less, it is.)
2) Call Apple and bitch at them enough that they send you Tiger on CD.
3) Install Tiger. Preferably after backing up and wiping your hard drive clean, as an upgrade from 10.1 -> 10.4 would likely cause more problems than it fixed unless it was a clean install.
4) Be happy that you've pulled another year or so out of a very old (but still pretty!) machine.
A final word: I think ND is right. If you keep your eyes peeled, you can get a low-end Mac Mini AND decent LCD monitor for about $600 (either through Apple+craigslist, craigslist alone, ebay, or whatever). This will be about 2-3 times as fast as the iMac, so you could use it for another 3-4 years or so. Now, upgrading the RAM on your iMac to max and installing tiger will probably only cost about $200, so it's cheaper in cash now, but the time, effort, and hassle involved may make it worth the extra cost to upgrade now.
And that's all the advice I have.