Hi!
It all depends on how confident you are with Linux and it's configuration. Printing on Linux isn't poor if you're printer is supported as it can run CUPS (Common Unix Printing System) which is well documented and easy to administer if you know what to look for. Also, a lot of the different flavours of Linux run their own print packages, of which some are good, some are bad. I tend to stick to CUPS though. It's a preference thing really - some people I work with just use the OS print service (lp) just fine.
Also, if you want to get started in Linux and consider yourself to be a "newbie", then take a look at
www.linuxquestions.org - this forum is superb and there are some excellent people on there who would be all to glad to assist you.
My overall advice though would be to use your PIII to learn linux but set up another machine to be your print and file server for now. Once you've got to grips with how Linux is configured, and you're reasonably confident you can get it to do what you want, then go for it!
The networking side - doesn't really matter. Would recommend the MAC suggestion if you're using Wireless as turbanator said.
If you need any other help or decide to go for the Linux option, feel free to ask any questions!
Kindest regards,
Calski