In many ways, this depends on how hands-on you're willing to be with the administration and learning the underpinnings of the software.
If you want a machine that is more akin to an appliance, then OpenFiler or FreeNAS may be more appropriate for your needs. The former is based on rPath Linux, the latter on FreeBSD. Both provide web-based administration interfaces to help you set up your file server. The big win here is that you don't need learn everything about everything to do with file server configuration (this can save a lot of time). The downside is that you're giving up really fine-grained control of the system.
If you want to manually manage everything on the machine, then Debian, Red Hat Enterprise Linux (RHEL), or CentOS would all be a good selection. I would probably lean towards RHEL/CentOS because its stronger enterprise bent gives you a better chance at there being a lot of existing tools to do what you want. The documentation archive for CentOS 5 may be a good starting point to see if there's some additional tools/docs that can get you started.
If you don't want to use this as a learning situation, but just need something to work, then I would strongly suggest going the OpenFiler route.