A PowerPC Mac with a 1 GHz processor either has a factory-installed G4 processor or has a G3 upgrade card installed. In either case, the machine can quite comfortably run an older version of Mac OS X that supports PPC processors (at the time of this writing, all that leaves out is the latest release, OS X 10.6 Snow Leopard, which drops support for the PPC platform altogether in favor of Intel).
My mother uses a 933 MHz G4 running OS X 10.5 (Leopard) all day long to surf the web and do other basic computing tasks; it's never been slow. My home network server is a 733 MHz G4 running OS X 10.4 (Tiger) Server (and I'm hardly your "average" home network user). If your machine is one with a third-party G3 upgrade card, you may need to hack the newer versions of OS X to run them, but this is a relatively straightforward process, and you won't have any performance problems once you get it installed. Otherwise, you can install a full retail copy on a G4/1GHz without any extra effort.
Remember that RAM (not processor speed) is key to making Mac OS X run at peak performance. Make sure that you have at least 512 MB, preferably 1 GB. Chances are very good that your machine uses the old standard PC100/PC133 168-pin SDRAM, which is available for extremely reasonable prices nowadays. Pick up as much as you can afford, and cram it in. (A good idea even if you run Linux.)
I highly recommend this route if you/your friend is not already an experienced Linux user; one of the major appeals of the Mac platform is the operating system. My not-so-humble opinion is that Mac OS X absolutely blows away any Linux distribution, even for the hardest core UNIX fans, considering it runs on top of a BSD UNIX-based kernel. Running OS X also solves the problem of modern browsers not being available that you would otherwise face by sticking with Mac OS 9. Your machine is not old enough that you're consigned to running a Linux distro on it just to make it barely usable on the Web. Apple's Safari (included with OS X; be sure to download the latest version) is an incredible browser on the Mac (less so on Windows), or you can run Firefox, Opera, OmniWeb, Chrome, etc.
If you're sure that you want to run a Linux distro, you truly have countless options. Again, your hardware isn't old enough to limit your options, and almost all of the mainstream Linux distributions (and some of the not-quite-so-mainstream distributions, as well) have been ported to PowerPC. You might find this site to be interesting. In general, I would probably select from one of the following distros: