If your are just trying to send files to others and not receiving anything, then I would just use the built in Web server on server 2003 and make a web page to the files your want.
But if you want it to be more like a shared drive I would go with FTP. Not sure if server 2003 has a good FTP server built in, but FileZilla (filezilla-project.org) is a grate free FTP server program for Windows systems. You can even get secure socket layer (SSL)working with FTP if your want more security.
Ports to unblock from the server's firewall, and to port forward to the server. (by default)
20,21 for normal FTP and also 990 if your want to add SSL to your FTP.
I think there is a range of ports your need to open, but your choose what they are in FileZilla.
a good FTP client program is FireFTP it can access a SSL FTP. It runs right in Firefox