I've added two of my email accounts to Thunderbird, but it's only downloading my unread messages, how would I set it download everything so that I can have a record of all my emails?

No idea what you have already set but;
in Account Settings -> Server Settings uncheck "Fetch headers only" and "Leave message on server" should make it download all the mail.

OR

You may need to reset the account from IMAP to POP

Thanks