It’s more than likely that your email provider of choice, especially the ones that offer mail services free of charge, will not support receiving email to custom domain names like, in my case, davd.net. Running your own mail server would solve this problem but running a fully featured mail stack including POP, IMAP, Sieve filters et cetera requires a fairly powerful machine. Additionally, if not configured properly, there’s big potential for abuse, e.g. spam.
As an alternative, it’s possible to just run a MTA which redirects all incoming email to an external mail server. This can be ran on almost any machine, even on a low-budget computer like the Raspberry Pi or a cheap virtual server.