...or through Godaddy since they are already hosting the website?
Wouldn't your hosting package already include email service? (POP3/SMTP/IMAP)
I would think so as well and I would suggest IMAP connection versus POP3 though.
One leary thing with Google that I have is all that info that is flowing through those servers. I'm leary of having even more. If I was competent on my own, I would host my own. Tin foil hat time I know.