I'd go with Debian netinstall from the stable branch. What are your specs? I've pretty much set up something similar. Its amazing how much I can get out of this ancient pentium II 350 / 160 MB RAM. I have a TV capture card installed in it and I can stream wmv/mpeg4 at 320x240@25fps - its quite viewable
Concerning file server - (s)ftp would be enough? If you need access via http then I'd suggest lighttpd, as has been said apache would be overkill.