Looking at Hover, the email solution linked to a domain you get from them seems the simplest way to go. I have no idea about the quality of the spam filtering, power tools etc. I personally have used Fastmail for the past 15 years and love what I can do with it. (But I’m not a normal email user and my family members have no need of that configurability.)
If price is a concern, Hover’s $5/yr email forwarding is the way to go. Keep your gmail or iCloud or whatever you like these days (and your individual family can as well.) Forward mail from that address to your preferred service - and if you want - configure your service to send mail with your custom domain. It’s a one time setup and forget it sort of thing for most people. And for a family of four, it’s the same price as a regular small hosted account for a single person.
I host my extended family’s email on an old 250 account GSuite account that I got for free a while ago. I’ve thought about moving to something more privacy focused, but none of them want to change how they get their mail, and I don’t want to pay for something that satisfies my preferences but doesn’t matter to them at all. If I were doing this today, I’d set up the forwarding service for each the family members and call it a day.
If price wasn’t as much a concern (and people didn’t mind using a regular client to get their mail) Hover’s small mailbox service should be plenty for most people.