I'd definitely recommend both sendmail and postfix as good choices for MTAs (in preference to rmail, qmail, exim). IMHO, postfix is easier to configure, but I'd look at Sendmail for very high throughput applications.
If you're planning on implementing support for a large organisation (or a lot of sites) then you might want to have a look at running an LDAP system to route mail.
sysadmin1138's answer is a bit misleading - an MDA is NOT a milter, and a milter is NOT an MDA. A milter is policy tool for an MTA. Milters and the milter API were originally proposed and implemented by Sendmail - but IIRC are binary compatible with Postfix. Its a good idea to add in some security milters for incoming mail (spamassassin, anti-virus) and if your processing large volumes of messages, something like milter-limit to throttle output.
As for MDAs - there's lots to choose from. Procmail usually comes as standard on most Linux distro's these days and provides a huge amount of flexibility / configuration for routing messages, auto-responders, and out-of-office handling. Out of the box, this will write mail into mbox or maildir formats so they can be picked up and presented via a POP or IMAP server.
Which brings us neatly to the POP/IMAP server - the UoW one which comes bundled in most Linux distro's is OK for small workgroups, but for larger installations, you might want to have a look at Dovecot or Cyrus.