For added anonymity, if you're really cautious, you could always use a VPN anytime you visit one of the email services recommended in this thread.
For instance, if you decide to use Tutanota, activate your VPN prior to going to the Tutanota site, but specifically make sure your VPN is active when you login. If for any reason Tutanota ever got subpoena for information (likely cant happen since I believe they're in Germany), your Wide Area Network (WAN) Internet Protocol (IP) address issued by your domestic US Internet Service Provider (ISP) would never be known. Your WAN IP is how someone would track you down on the internet.
I use Froot VPN and have no complaints. Plenty of other options out there.