Hi
Hmm...Smart host, Relay hosts are terms usually referring to servers,
which are allowed to send emails to the public (smart host) or send emails
to the corporate mail server (relay host). In this context, the smart host
and relay host are in a different "zone" than the corporate servers,
e.g. DMZ (smart host, relay host) and LAN (corporate server).
The goal is to separate hosts facing the internet from the "inner" LAN.
(edit: oh god, sloppy 5' language...

)
Any mail server should be able to send emails without this kind of extra
configuration. Again, be sure you got protection from the managment,
when you are setting up a mail server for your company...
Try first to send an email to a local account, using a local account.
Test the connection "to the Internet" by establishing a connection
to a known mail server on port 25, which is the only port required
at the moment.
Good luck
Cheers