You need to see whether the app supports 10.4.11 and it is either a Universal app or written to support the PPC.
There are lots of these apps around. Post another question here to ask about the app you are looking for.
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
iCab - The Taxi for the Internet
http://www.icab.de/
What is my user agent?
http://whatsmyuseragent.com/