If you want the security and privacy features of the above solutions while not paying too much, Rackspace offers the best alternative. In fact, they claim “256-bit Encryption in transit and at rest.” Rackspace offers a basic plan at $2/user/month, with huge 25 GB mailboxes, 30 GB cloud storage and unlimited email aliases. You can run your emails from Apple Mail, Mozilla Thunderbird and Microsoft Outlook.
Things are probably more complicated than that, though. As a recent survey conducted by market research firm Statista clearly shows, email is one of the most popular apps for mobile devices across most organizations and even consumers. Given how many workflows, business processes, and just plain important communications take place over email, this is one area where you likely shouldn't skimp.
In terms of security for its hosted email services, you'll find this is all hosted in Microsoft's data centers. That means you'll have all the same security benefits as those provided to other Microsoft Office 365 users. Your email data will be encrypted in transit and at rest using SSL and Bitlocker technology. Per Microsoft's publicly available terms of service, Microsoft employees only have highly limited access to your data and only under specific, audited circumstances.
If privacy is your number one concern, perhaps you should go with Protonmail. You can upgrade to an email with your domain easily on a web interface under “Protonmail Plus” or “Protonmail Visionary” plans. However, the plans can be rather expensive, as getting only 20 GB storage space could cost you at least €24/user/month/yearly. Most email hosting providers retain your emails for months even after you delete your account. This Swiss email provider will destroy all your data when you delete your account. 

Along with the slew of desktop apps, you also get access to Microsoft Outlook Web Access (OWA), a sleek and modern web adaptation of the Outlook email client. It offers a familiar layout for calendars, contacts, and tasks, and a new "focused inbox"—all available in your browser. What Microsoft means by a "focused inbox" is that, rather than just being a dumping ground for all incoming email, it defaults to a dynamic view that's constantly being updated. This tech is based on a machine learning (ML) algorithm that attempts to figure out which email is most important to you; everything else goes to the regular inbox. As you sort emails between the focused inbox and the regular inbox, the algorithm gradually gets better, helping you to concentrate on email that matters most. You'll also be able to use mentions. When creating a new email, if you prepend someone's name with the @ sign, then it will automatically Cc that individual. You can also apply a filter that will show you emails in which you were directly mentioned.
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