Yes, in order to receive email, you must install a mail server such as Postfix. As far as gmail goes, you can set that stuff up with gmail without having to enable forwarding. Under settings you can add a new account, here is where you can add another email address that gmail will both send and receive mail as. I have over 10 email addresses that gmail takes care of that have my domain.
It is possible to forward emails to another email account using pretty much any mail server, but since I've never done that before, I'm not sure how to. As soon as I figure it out, I'll post back.