Hangdog 42 is right on. For what you need any distro with Samba would probably be OK. You should consider the hardware and go toward a smaller distro if you have older hardware. For just backing up files, I use NASLite http://www.serverelements.com/naslite.php
to an ancient (166MHz) POS, but it's pretty limited really. I've used RedHat 6, Feather, Damn Small, now Vector, all with Samba so I could do backups from my WIndows box. Just pay attention to the password stuff in samba, it trips a lot of people up. It's a very well documented package.