How to import messages to ThunderBird from Outlook 2003?
From my last experience I can say that the easiest way is to import/export this way:
Outlook 2003 -> Outlook Express – > Thunderbird
Next step could be using MozBackup application to make backup (export) database, eg for deploying on other machine.
How to export messages from Outlook 2003 to Gmail?
Just use dedicated Google Application: Google Apps Migration for Microsoft Outlook
From my exprience – export of 250 000 messages took 7 days (no matter of the Internet connection speed).