Fundamentally Godaddy is the mail provider and Thunderbird is the client. As a client it connects to the provider and get mail that the provider has received and connects to the provider to send mail you write. To use a car analogy. Your car is blue (Thunderbird) and is from Ford (godaddy). You want to change the Ford into a Chevy. This is not something that involves Thunderbird. It will get mail from any provider you sign up with. But as godaddy is a domain host, I am guessing you have a domain registered to them, so you will be looking for a new domain hosting service, or at least an email hosting provider if you want to get rid of godaddy only for email. I suggest you look for recommendations for a good hosting service. Google is full of them, but I have no idea which are good.