Having said all of that: I personally think it's a terrible idea to use old versions of Mac OS X on the Internet, and if you're looking at an Internet computer, I personally recommend sticking with a "pretty recent" version of Mac OS X, which will run well enough on a perhaps surprising range of hardware.

It's a calculated risk and there are ways to mitigate it, but there's more interesting things to be done with a G4 than to check your webmail, and faster and safer hardware on which to check your e-mail.