Disagree with 99% of the other posts. If you self-host your email it is archived on your system. So-called “private” email isn’t after 6 months in the US. And it is more stable and higher performance to run my own Roundcube webmail on my own server. And I can control the spam filtering. All reasons to host your own.

However there is some “maintenance” involved with unscrupulous black list sites and overzealous email filter software. Google likes to declare basically everything not coming from their buddies as spam Microsoft wants you to kiss the ring. On a work account just this week I tried contacting a German company called Beckhoff and after just 3 “dead” email accounts from previous contacts they decided to ban my entire company (about 100 employees, been in business over 75 years). They also don’t answer their phones. Not sure if they’re still in business or just being German jerks. As a result of their poor performance we may switch to a competitor. I do not put up with that crap.

Also I’m not sure how to phrase this politely but despite promises unless you are using PGP to end-to-end encrypt your email, and even then it’s not 100%, you can’t ever totally make it private. Also it is impossible to totally ensure identity of the sender although we’ve come a long way. Protonmail recently published how they delivered a criminal to the authorities using the small amount of public information they log.

As a result I do agree that you should let someone else deal with the black listers, bans, etc. But I strongly disagree with keeping it on a remote server more than about 10 minutes. That means one of three options (for receiving:

1. If you have a static ipv4 IP use the email service on Cloudflare to act as a mail relay and forward email to your server. Thus Cloudflare’s reputation not yours is what matters.
2. If you don’t have a static address, you can rent a VPS. Low end box (lowendbox.com) has some great coupons all the time. You can get easily under $12/year. In this case tunnel from your actual server to the VPS. We really don’t “need” the VPS.
3. Pay for a forwarding server. I used Dynu in the past. Never had an issue. It was I think $10/year. Again this assumes you have an accessible server on a static or dynamic ip. And you are basically paying for what Cloudflare does for free.
4. Pay for webmail. Again Dynu is $20. Then just program your local webmail to call imap and download everything say every 5 minutes. But it limits you to ONE user or each user doing their own thing.

On server dovecot and sendmail work well. Roundcube looks exactly like an improved gmail.

For sending I use smtp2go. At my low usage entire family is free.