My own mailbox / Mailgun smtp

Your domain points to a nameserver. On this nameserver (whichever you’re using), the configuration for a website and email are two different things. You use a “A record” to point to the IP address where your website is, and you use “MX records” to point to where you’re receiving emails for the domain.

So in principle, shouldn’t be a problem. Now, some registrar only provide email if you’re actually using their nameservers. What you could also do, and point to D.O. just for the website.