For the most part, you should be able to handle mail using your ISP's POP servers and SMTP server. However, for a variety of reasons, I am now running several mailboxes on my system and wished to set up a hidden mail system. Below lies madness.
What I have done is configured my Solaris system so that it acts as the mail server for my internal network. At intervals, my local mail server checks the mail boxes at my ISP's mail server, downloads any new mail and then places it in appropriate mail boxes locally. From there, any local mail clients can pick mail up from my POP3 server. Similarly, any mail being sent is passed through my sendmail program, which handles any aliases, redirects any local mail and passes the rest on to my ISP's sendmail.