I use an iMac G3 for games, but it definitely has problems, including a Sherlock 2 alias which refuses to run from the Apple menu (despite the alias being up-to-date), choppy sound (not found in Classic Environment), a partitioned hard drive, and a few others. See, around 2002 or so, the hard drive died, and when it was changed, the hard drive was partitioned, with a Mac OS 9 side (about 2GB) and the Mac OS X side (about 18GB?). The Mac OS 9 side was sort of messed up, with things removed deemed not necessarily (my brother and father's handiwork). Even after an upgrade to Mac OS 9.2, it still has problems. Choppy sound? Yes. A strangely jumpy mouse whenever the Mac OS X partition is opened? Yes.
What I want to do is not merely delete the hard drive and start over, but really start over. Make the iMac new again (well, not really). You know, with the "Welcome to your new iMac, want to get on the Internet?" dialog? YES, that one! How would I go around to doing it? (and assume that I found the original boot disc).
Which iMac are you talking about? And how much RAM is in it? You wanted to install OS 9 or X? Just wipe the hard drive clean with a reformat--write zeros over it--and reinstall a system. That'll take you back to square one. The symptoms you describe might be bad RAM, though.
Normally I've said install Panther on an iMac, but there hasn't been any updates to Panther in years now, so I usually have 512mb RAM in an iMac DV now and install a hard drive with Tiger already installed on it from a G3 or G4 tower. I don't think you'll be able to successfully install Tiger on an iMac G3, or if you can, it will be a big hassle. The first generation iMacs, though, with their Rage II video cards I wouldn't go above Panther.
Check to make sure the firmwares are all up to date. You have to do that all in OS 9.
I went looking for the iMac firmware update on Apple's site, but found this forum which looks like it covers most of everything:
http://discussions.apple.com/thread.jspa?threadID=1787702
It's a mid 2000 iMac G3 that was the high end iMac at the time. I deinstslled X on it recently...for me it had no purpose. If the RAM was bad it would've affected all parts of the system. I guess that in my case, the best opprotunity is to back up, reformat the drive, and boot from the CD.