I've recently brought back a Blue and White Apple Power Macintosh G3 to life, and I was going to put a flavour of BSD on there (instinctively), but I changed my mind and decided to dump Mac OS 9 on there, for nostaligic reasons ;).
Anyway finding a basic web browser that's still being compiled for that OS is a real challenge, but some digging around did produce some links:
This is the 2003-07-21 release of WaMCom, the Web and Mail Communicator.
Information regarding unicode support in Mac OS 9 browsers; it’s actually very useful simply because it lists all the browsers!
More when I find them.