In my experience, I left my iBook G3 800 MHz in Mac OS X 10.3.9 and bought an iBook G4 in order to run Mac OS X 10.4. As usual, when buying used iBooks on eBay, I chose ones which included the original system discs with it, even if that meant paying a little bit more.
Mac OS X 10.3.9 is perfectly capable of running apps in the Classic environment (assuming it as been installed) as well as booting into Mac OS 9. (With an iBook G4, dual-boot capability is lost.)
Do you have the discs that originally came with the iBook G3 800 MHz? I believe yours is a newer model than mine, and would have come with Jaguar pre-installed, so the original discs would be for Jaguar. Even Jaguar supported Classic Mode (as well as dual-booting between Mac OS X 10.2 and Mac OS 9).
When installing Panther, you have to check a box to install OS 9 drivers, if memory serves me correctly.