With a 1.67 GHz PB G4 you can upgrade to OS 10.4 (Tiger) or OS 10.5 (Leopard).
Do you use Classic? If so note that 10.5 does not support Classic.
If buying from eBay or wherever make sure you are buying the black installation disks (usually referred to as 'Retail'), not the grey ones which are model-specific.
Those disks will probably not be the last version of each OS (10.4.11/10.5.8) but once you have installed the new system you can update to its latest version via a download from Apple.
Before upgrading, check the startup disk.
Launch Disk Utility. /Applications/Utilities
Select MacintoshHD in the panel on the left then select the First Aid tab.
Click: Verify Disk (not Verify Disk Permissions)
If the startup disk needs repairing, follow the instructions for Using Disk Utility to verify or repair disks.
NEW Apple Mac OS X 10.4 Tiger FULL Install DVD
This is what I have found on ebay to purchase...
That's the link. $85 for the disc.
I know i can probably downloaded somewhere for free but given that I am pretty clueless i am worried that if i don't get the real deal, it won't work and worse of it, caused more problems.
Also, there appears to have different version, the only reason i picked this item is because it says it is full install version. There are other versions on ebay, such as 10.4.6 and 10.5 etc...again because this powerbook being a bit older, am not sure if would work.
Thank you again for all your fab suggestions already. I knew i am in the right place joining up!
If you purchase an upgrade to 10.4, once you install it, regardless of which release it is, I'd recommend you then install the combo 10.4.11 update, which will bring it from any version of 10.4 to 10.4.11. While you have to buy the 10.4 disks to upgrade, the combo update is free from Apple, and can be downloaded from http://support.apple.com/kb/DL170 .
You would launch Disk Utility, repair permissions, install the combo update, the repair permissions again. Done! Then run Software Update to catch up on any other updates needed. The reason for using the combo update is, rarely, the Software Update function doesn't function quite correctly, which can lead to odd behaviour that you don't want in the operating sytem.
On your system, while 10.4 will work with 1GB, I would consider adding to the memory. Take it at least to 1.5GB or even max it out at 2GB.
Alice- You've received good advice here already. Allow me to add one further suggestion:
Don't do this.
Your computer is pretty long in the tooth. $85 is not a lot of money, but it's still $85 that could go toward a replacement MacBook or MacBook Pro or some other Mac. It doesn't have to be a new one, but unless you absolutely have to run old Classic applications (very unlikely in 2011), then that $85 would be better as a starting deposit in a savings account that you'll add to until you can afford a decent used Mac with a Core2Duo Intel processor or better.
If you want to stick with your current computer, for whatever reason, then consider purchasing Leopard (10.5) instead of Tiger (10.4) as long as you don't need to run Classic applications. You should be able to get 2gb of RAM into that machine, and with Tiger or Leopard it will run much better with that second gig.
10.3.9 is not the worst OS in the world - I'd rather use it than any Windows OS. It's a very good choice for your current computer, as long as you run a decent web browser and keep it maintained (via Disk Utility) and updated (via Software Update). Upgrading the OS (and the RAM) might be a good option, but the limitation on "new" software you can run will be bounded by the hardware, not the OS, because it uses a PowerPC processor rather than an Intel processor.