Welcome!
As most browser versions are tied to System Software versions, you are limited. PowerMac G4s (the newest are now 14 years old) are limited to no higher OS than 10.5.8 if the processor is 867mHz or faster, or 10.4.11 if it is slower thatn 867mHz. "Big-name" browsers left the PowerPC behind long ago.
Your best option is TenFour Fox. It is a FireFox "fork" written to run on PowerPCs. I still have several PowerPCs connected here and that is the only browser that comes close to working. Because it is forked from recent versions of FireFox, modern web pages see it as "supported" and you don't get those "browser is too old" errors.
This is the developers' site:
http://www.floodgap.com/software/tenfourfox/
Do not get TenFourFox (abbrev "10FF") from anywhere else. Too many download hosting sites today will fill you up with adware when you download something.
EXPECTATIONS (and what not to expect):
- You will not have a smooth browsing experience. Even with the magic 10FF brings, web pages are no longer optimized for the now-primitive processor in your G4; that processor will struggle with decoding the pages. Page loads for me are slow for me even on a directly-connected 100MBps cable internet service, and scrolling or redraws will give you time to contemplate the wonders of creation.
- 10FF does not support plug-ins. You can't watch Flash videos or do things like NetFlix. It does support many FireFox add-ons like ad blockers, themes, etc, so it's not dead, just a little crippled by the way web pages are now created.
- You will not get the current Mac experience with a G4 (made from about 1999 to 2005). To see what it is really like, I think you need at minimum a 2010 or later model Mac.
That said, there are those of us here who love our G4s and try to keep then relevant. We can toss out some useful tips if we know the sub-model G4 you have. There are G4 PowerMacs (mini-towers), G4 iMacs, G4 "Cubes"; and G4 Mac Minis, in the desktop category. plus PowerBook and iBook G4s in the laptop arena. Some are very easy to service at home. To that end, please find the sticker on the case with the serial number and enter the number into this support page to get the sub-model:
Check Your Service and Support Coverage - Apple Support
If that tells you it can't find the model, this web page does teh same thing but goes back farther in time:
https://everymac.com/ultimate-mac-lookup/
If that fails, snap an image of the computer and post it.