I've just updated my 'new' G3 500mhz DV SE. Can't help you with OS 9 but can give my experience of getting to Tiger...
Mine was more or less untouched from when it was bought - hard drive had never been wiped in it's 11year lifetime and was still running OS 9.0. I've never used OS 9 (I'm a 'newskool' Apple user!), but wasn't too bad with PC's back in the day so suspected it wouldn't be too hard.
Firstly, if you are running less than OS 9.1 you need to upgrade to 9.1 (I was at 9.0!) - download the correct 9.1 from Apple here for free if needed - the update you need will depend on the version you are currently running -
http://support.apple.com/kb/HT1387
You can then install the updated 4.1.9 firmware from here -
http://support.apple.com/kb/DL1283?viewlocale=en_US
Make sure you follow the update instructions.
I then obtained a copy of OS X 10.4 (Tiger), rebooted the machine (hold c key at the 'chime') and completely wiped the drive during the install.
It runs pretty well - much better than I expected in fact. I've given mine 1GB RAM, but looking at the Activity Monitor, if all you are using it for is a bit of word processing, iTunes and general light use, 512mb would be enough. I have disabled Dashboard and Spotlight via disabletigerfeatures (Google it) and have installed ClickToFlash. If you want a decent word processor get a copy of MS Office vX.
Hope that helps a bit.