James, in response to an early post, I gave a general guideline
Macs before and including the 17 inch flat panel iMac (about mid-2002) could boot up under OS 9, and Macs including and after the Power Mac G3 (blue & white) (early 1999) could run Mac OS X, and can probably be upgraded to 10.4.11.
But I also recommended that you download the Mactracker application at www.mactracker.ca
to check out your specific model.
Later, in response to a question from John Rougeux, I think you confirmed that your model is probably an iMac G3/350. John provided a link to everymac.com
If you scroll down to "Pre-Installed MacOS" and look to the right at "Maximum MacOS" you will see 10.3.9
Before you purchase 10.4 or attempt to upgrade, please do this:
 Download www.mactracker.ca
 In Mac OS X , open System Profiler from Applications -> Utilities. Check your Model Identifier.
 Open Mactracker.app and search for the string from Model Identifier.
 The field Maximum Mac OS should tell you how far you can upgrade.
For example, if your Model Identifier is PowerMac 2,1 and you have the 350 MHz (non-Firewire) model, the maximum Mac OS you can install normally is 10.3.9. If your have the 400 MHz model with FireWire, then you can install 10.4.11.
Because you may be on the edge, please check this out before you spend money or attempt an upgrade.