If you go the Linux route with a simple shared file server, you'll need Samba. Of the smaller Distros, Puppy Linux has a small memory footprint and also has most if not all of the programs you'll need precompiled. Fedora 8 will work well though 9 and 10 seem to be buggy in some areas. I haven't tried 11 yet.
Otherwise,you could use Win98 and even Win95 for a simple file share system. The suggestion here would be to create a second partition on the drive so that the operating system could be completely isolated from the shared section of the drive even though the sharing system allows individual directories and separate passwords for each share.
If you need to have more secure and limited access, back to Linux and the configuration gets interesting. While there are tools that will help you configure Samba, I haven't found any that actually do the job. I always end up manually changing the configuration. Keep in mind, there was a whole book published just on Samba and it's pretty big.
I have an FTP/Apache/Samba file server running off of Fedora 8 at work on the local network. If you think configuring Samba is fun, you should do Apache, Samba and FTP so that they all work on the same file share path. Mostly I have Apache serving up the files and FTP just to add files to the read only part of the server. Samba still isn't working the way I want it to work.
The really bad part is it was mostly a wasted effort and the files are still served off of the Win98 machine that I started with around 10 years ago. No one likes change. The Linux system is actually easier to use even though it is protected better and a little more difficult to add new files. Configuring computers or in fact doing anything other than the bare minimum to keep them running is "a waste of time." So I'm usually fixing a crisis when things stop working.
Shadow Wolf