You are correct. You need to check out the firmware level before installing os x 10.3.
Open Firmware, boot into Open Firmware.
Power on your iMac while holding down command+option+o+f
The first output line contains the firmware level. Mine reads:
Apple PowerMac4,1 4.1.9f1 BootRom built on 09/14/01 at 13.18.04
Copyright 1994-2001 Apple Computer Inc.
On my machine, I have 4.1.9f1.
What firmware do you need?
http://support.apple.com/kb/HT1395
You can download the firmware from this page:
http://support.apple.com/kb/DL1283
filename: N-iMac_FWUpdate_4.1.9.smi.bin
avoid expanding the file on the download computer.
For a slot loading iMac, this article indicates that you need to be running 9.1 or later version of Mac OS Classic.
http://support.apple.com/kb/DL1283
"The iMac Firmware Update 4.1.9 will only run on iMac computers with slot-loading CD or DVD drives running Mac OS 9.1 or later from a local drive. If you are using Mac OS X you must boot from a local Mac OS 9.1 or later writeable partition (not a CD, or network disk) prior to following the update instructions."
You can download the Mac OS 9 updates from the Apple site.
http://support.apple.com/kb/HT1387?viewlocale=en_US
For tiger, you need 256meg of memory. A slot loader will take 1gig of memory.
You may need to get more memory.
get the 512meg card(s)
http://eshop.macsales.com/shop/apple/memory/iMac/G3_450MHz_500MHz_600MHz_700MHz
Mac OS X 10.4: System requirements
http://support.apple.com/kb/HT1514
PPC 10.4.11 combo update.
http://support.apple.com/kb/dl170