I backup my entire email, address book etc quite often using a program called "Outlook Express Freebie Backup".
Its very easy to use and takes the hassle of doing it all manually.
Backup your entire Outlook Express details from the old computer, copy the backed up files and the program to the new system, then use the 'Restore' feature of Outlook Express Freebie Backup to put it all back on the new system.
Search for it with Google, and like the name suggests, its free.