OS 10.5.8 is as far as a G4 PB can go.
Anti-virus? Short answer is no, many (most?) people don't or just use something free like ClamXav which is well regarded. Long answer is that there are other things besides viruses that go bump in the night and reading this may help.
Try TenFourFox as a browser.
Bear in mind G4's and 10.5 though capable for many uses are now old in computing terms and may not be a good comparison with a modern Mac.
A PowerBook G4 is quite limited at this point. Don't get me wrong, that was a great machine... I still have one that gets regular use. However, you can't upgrade it past 10.5.8 and it can't do many things that a newer machine can do. The system has changed a fair bit between 10.5 and 10.8. And since it has an old PowerPC processor, rather than the Intel processor that Apple's hardware has used for a very long time now, it cannot run a lot of newer software. So, as Michael says, it may not be the ideal machine for learning about modern Mac systems. But it'll give you a taste of the Apple, at least!
As for anti-virus software, see my Mac Malware Guide. If you do want anti-virus software, since you're stuck at Mac OS X 10.5, your options are limited. I'm not actually sure which AV software still supports PowerPC machines. I think ClamXav does, but it doesn't do the best job of detecting Mac malware. (See Mac anti-virus detection rates.) Fortunately, you may be safer than most, because almost all recent malware has not been capable of running on PowerPC chips, and older malware that can affect a machine with a PowerPC chip is not still circulating. So the age of the machine may be to your benefit there!