"Private" and "email" should really not appear in the same sentence. The email protocol was not designed with privacy in mind, so any company offering you a "private" email service is simply pandering to the privacy-conscious crowd. Yes, some may promise to store your messages with "zero access encryption" and end-to-end encrypt messages between users of the same service but unless you're only messaging those users (not gonna happen) copies of all your messages will be hanging around on much less secure/private servers.

Tutanota, Protonmail and Lavabit are currently the most known services promising private email (I have personally opted for Protonmail because it's free and does not require invites) but you're making a mistake if you want to use email for any sort of private or confidential communication. Use mail to create an account on with a service designed with privacy in mind, sure, but don't try and twist email into something that it isn't - you will regret it.

My general philosophy with email is to use a service which would go out of business if it was found out that they've been giving 3rd parties access to your messages and even then don't store anything sensitive on mail. The ones mentioned above will do fine for that.