So, what I did for a similar use case:
-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)