1. The best way to store emails in the best readable form is in my opinion: print them as a PDF to your storing media (intern or extern harddisk, usb-stick or the like). Just right-click on the email, choose 'print', then choose 'post-script' as printer, and it will be printed to a folder called 'PDF' in your 'personal folder'.
2. What Thunderbird actually saves or not, find it out this way: Open your 'personal-folder', then press Strg and 'H' together, and you will see all hidden folders, including /home/yourname/.mozilla-thunderbird.
Open it, then open /home/yourname/.mozilla-thunderbird/ymn7k9o4.default
and check the 'mail' folder. There you find, what thunderbird stores and how it does.
But I don't know any other way to export emails, which is easily readable, other than PDF,.
If you want to save all emails including your configurations, i.e. if you are installing a new system or just for saving purposes, or if you want to export them in a way that it is easy to reinstall, just copy the whole .mozilla-thunderbird folder to your storing media. Once you installed a fresh thunderbird, just reimport this folder back in your personal folder, and everything will be done as before, nothing to configure.
If you just want to store the emails, you could also try to check the inboxes in .mozilla-thunderbird, but I have not done it, as the above way is much easier and faster and safer too. If you want to try anyway, watch out: How many inboxes you have and where you find them, depends on how you get your mails. Imap? Pop3? You don't have to bother, if you save the whole folder.
The other thing is, that your provider may store your emails, or in some countries he has to for a certain time. I don't trust my governement, do you?
Think about encryption (one nice easy one click provider: freenigma http://www.freenigma.com/
). Or add 'enigmail' from synaptic to thunderbird (include enigmail-locale-your_language). It allows you to sign your mails, in order to make sure the recipient knows, YOU wrote this mail. Enigmail allows you to create keys for strongly encrypted, safe and unreadable communication with others. Even if the mails are stored or spyed out, nobody than you and the chosen recipient will be able to read them, they'll only get numbers in case they try. But same for you, if you loose your key (Print the mails to PDF ...)
But the ones you want to exchange encrypted mails with, have to do the same, in order to be able to exchange keys and exchange encrypted emails and to be able to open and read them.
Hope I could help.