Powerbook G4s are quite capable when it comes to the internet, even word processing, spreadsheets, and some older games depending on what you want to put into it.
500 Mhz to 800 Mhz models can go up to Mac OS X 10.4.11.
867 Mhz and higher (1 Ghz is higher) can go to Mac OS X 10.5.8, but eliminate the Mac OS 9 application compatibility when taken to that level. There is though this tip on dual booting Mac OS 9 and Mac OS X 10.5.8 which is possible on some models:
https://discussions.apple.com/docs/DOC-1757
This thread deals with how to get the latest Flash browsing on your Mac:
https://discussions.apple.com/thread/4781929
This tip explains Java:
https://discussions.apple.com/docs/DOC-6491
Most Javascript will operate fine.
No Silverlight based video such as Netflix will work.
If you have data on it that you eventually want to migrate to an Intel Mac, use this tip:
https://discussions.apple.com/docs/DOC-2295