Look on the side panel of the iMac:
If all of the above ports are present, you are compatible with 10.4.11 Tiger.
The two ports above the Y like logo on the left are 6 pin Firewire IEEE 1394a ports, and are the only external bootable Mac OS X ports on PowerPC Macs.
If only the USB, ethernet, audio and modem ports are available it is compatible with 10.3.9 Panther.
Before you install anything, backup your data to two distinct locations.
Before installing any of the above, make sure you have the right firmware installed by installing the original Mac OS 9 retail installer disc. Also be sure that an authorized service tech has verified the PRAM/CMOS battery is current.
https://web.archive.org/web/20141113002136/https://support.apple.com/en-us/HT1395
Links for the firmware: 4.1.9 and 1.2
The retail installer disk looks like:
and should be installed first before the firmware is applied.
Once the correct firmware is applied, then you can install 10.3.5 retail or 10.4.6 retail:
Panther retail looks like:
Tiger retail looks like and came in both multi-CD release and a single DVD release that only external Firewire drives could boot on the iMac G3, unless the iMac G3 has a built-in DVD reader.
None of these discs should say upgrade, update, dropin, or OEM.
10.3.5 to 10.3.9 combo and 10.4.6 to 10.4.11 PowerPC combo can upgrade the respective CDs mentioned above once installed.
Disks may be unreadable also because the PRAM/CMOS battery is not current, or dirt or dust has gotten on the disc or drive or the disc is scratched. The drive may be cleaned with a slot loading cleaning brush CD that slides in. This cleaner does not have any solvents. Be very careful not to insert anything meant for tray only drives if you don't have a tray drive.
Note, you can't install Mac OS X from 8.6, as the firmware will not have been applied. Those iMacs without a back flap for a VGA external monitor will lose all access to the internal display if you attempt to install 10.2 or later without the firmware installed.