There appears to be two security issues in your post. The first is the security of your connection to the web server i.e. the security of your password/credentials. The second is the security of messages you send.
I suspect the warning you saw from thunderbird was about your credential security. If your POP and/or SMTP server require passwords and they are not using SSL/TLS, then those passwords are being sent to the server in clear text and could potentially be intercepted by someone else, giving them your password. If your service provider is unable to provide encrypted channels, I would change service provider. There are plenty out there which do. If you must use that provider, I would make sure that the password you use is unique to that service and not one you also use for other services.
The second issue concerning the security of the messages you send - bottom line, email is inherently insecure. You can encrypt your messages, but then people you send mail to must have the software to decrypt it and must have your decryption key (i.e. public key). Encryption of mail messages is supported by many mail clients these days and much easier than it use to be, but it requires additional effort for both the sender and recipient. You need to manage private and public keys and your recipients must be prepared to and able to retrieve your public keys and have a setup configured to use them.
There are no absolutes here. You need to consider both the risks and convenience aspects of email. What is the value of your messages to others and how difficult do you need to make it for unauthorised people to see your message so that the cost of doing so exceeds the value such action would bring. Encrypting your birthday greeting to your grandmother is probably overkill. There is unlikely to be any real value for anyone else and the inconvenience to her will likely be greater than the value of your message (not to imply she doesn't value your birthday wishes of course!). On the other hand, the email you sent to your accountant containing all your banking details has a lot more potential value to an unauthorised reader, so encryption would probably make more sense. Likewise, your accountat is also more likely to have support for accessing encrypted messages if this is their preferred means of communication (though I would personally still prefer a more secure channel for providing such information).