Yeah, exactly! You also brought up something that I probably should have mentioned too — it’s not uncommon that your domain registrar or hosting provider includes e-mail or offers it cheaply too.

Having the domain seems pretty critical to me and gives you a huge amount of flexibility — even if you just plan to stick with gmail, it gives you the option to migrate to something else in the future relatively painlessly. Your e-mail is your primary online ID, and not having control of it is actually kind of scary!