I keep an old phone on airplane mode with a backup of my 2FA codes in my Auth app in case my current phone dies. Peace of mind. Totally agree with the other commenter about using multi-factor authentication in most cases.
I do not leave myself signed in to Mail on my phone. I don't even have my accounts set up there. If I lost my phone and someone gained access to my signed-in Mail account, that would suck. I also stay signed out of Facebook, Twitter, etc. if I'm traveling anywhere.
I prefer LTE over WiFi in most cases, unless I'm on a trusted WiFi.