You can have this exact thing cheaper if you set up a server and forward your mail to Gmail. And you'll also have a server to host a website or whatever else.
Hmm, almost like Google have managed to make non-Google email impossible to do (excepting a few other very large outfits like Microsoft). What a happy accident that the de-facto answer is "give all your email to the advertising company".
-Buy domain from name cheap
-Setup email forwarding to my gmail account with namecheap
-Setup gmail to optionally send as dtparr@domain.name (I forget the steps, but I think it's under settings -> accounts)
So although the email comes to/from my custom domain, gmail is the real sender so I've not had any trouble with delivery (that I've noticed, at least)