I like and trust Proton Mail, and they support setting up custom domains while hosting your email data (for subscriber users).

You can then access it via their web mail box, via their Android and iOS apps, or via a desktop email client if you install their "bridge" application. The bridge application basically maintains the secure encryption ethos of their email system by ensuring all email traffic between your desktop and their servers remains encrypted, but can still be accessed via your preferred email clients such as Thunderbird or Outlook. The bridge is available for Windows, iOS and Linux.

I personally recommend Protonmail as it's primary focus is security and encryption, yet it does this in a very well developed and slick interface, so you get the best of both worlds. I'm a subscriber and moved from Gmail about 2 years ago as I wanted better privacy and security (they even have great tools for importing your old emails from major web providers). I don't have a custom domain but from my experiences of everything else they provide, I'd be confident it works as intended.

EDIT: In terms of cost, its €4 a month for the first tier which includes support for 1 custom domain, 10 email addresses, and 15GB of storage, or €10 for 500GB, 3 domains, 15 emails. They also include VPN, calendar, drive storage and a password manager in both.