I used to run my own mail server many, many years ago (early 2000s), but today it's a lot more difficult. I personally don't think it's worth it, but I do have my own domain that I can host anywhere I choose. At the moment, I'm using Fastmail. Lots of nice features, and no complaints.

On my home network, devices are backed up using Time Machine over the network. I also use Backblaze to make a second backup of data to their cloud service, using my own private key. Lastly, I throw some backups on a USB drive that I keep in a fire safe.

You definitely don’t need to worry about a web site if you want to just use the domain for email.

Feel free to hit me up if you have any questions about it. Some providers make it pretty easy I think to setup and manage all of that together, while others require some manual work on your part.