Interesting question! I haven't done the work (my Omega2s have yet to be shipped according to the schedule), but the server you need depends on your desktop OS. If Linux within a private LAN, a NFS server would be very efficient. If using Windows, a Samba server would be preferable.
If using around the world as the original poster requested, make sure that your security is top notch. Criminals absolutely love it when they discover file servers to dump and broadcast crapware freely using your Internet account.