Posteo may be best for privacy as third party provider: https://posteo.de

Other resources on webmail: https://www.fsf.org/resources/webmail-systems

For your self-hosted email, I recommend Courier MTA with Courier IMAP which is available on Debian GNU/Linux and other VPS/Server solutions: http://courier-mta.org/

It also offers pretty nice, secure webmail SQWebMail system.