Changing mail providers isn’t easy when you use their domain endings as you’ll probably have to update a bunch of accounts to use a new mail address. For the future, use email providers that allow to use your own domain(s), switching providers is a lot easier then. You can export mails from Gmail with ease though, as long as they provide IMAP you can simply sync your complete mailbox and you could even upload all of it to your new email provider.

And Google Drive…simply transfer all your files to somewhere else and done.