You shouldn't need to change your email address because you've changed your phone provider. I don't know your circumstances but it would be unusual to have to set up a new email address because of this.
As long as you know your email address and password from when you set up your original email account, you should be able to transfer the information to your new devices and carry on using the same address. Look up 'adding my email account to iPad and iPhone' on YouTube.
If you don't like your old email provider, you could open a second account from a different provider and run them side by side for a while so you have time to transfer contacts and emails you want to keep to the new one.
When setting up a new account you will be asked for a password and other information such as a backup mobile phone number for additional security. Make sure that you keep an accurate record of such information and keep it safe. Do not use the same password for both accounts.