Tiger is the last official release support on this machine. You can get Leopard to run on the machine with some 'macgic'.
TenFourFox -- It's a port of the latest FireFox to run on older hardware and software.
"World's most advanced web browser. Finely tuned for the Power PC."
-- works for me on 10.4. Supports 10.5
http://www.floodgap.com/software/tenfourfox/
alternative download site:
http://www.macupdate.com/app/mac/37761/tenfourfox
Turn on pipelining. This will allow Firefox to make simaltaneous requests to the server. Chrome has pipeling turned on. Some sites could fail to load with pipeling set on. The site will be old. See "Increase pipelining" in:
http://www.hongkiat.com/blog/firefox-optimization-tips/
OmniWeb uses the lastest Safari framework. The open source WebKit. Other browsers like Safari and iCab use the OS version of WebKit. The OmniWeb downloaded dmg includes it's own copy of the latest WebKit.
http://www.omnigroup.com/products/omniweb/
Safari 4.1.3 for Tiger
http://support.apple.com/kb/DL1069