Once you’ve downloaded all your emails, if you go to Tools > Export, you can back up your entire profile there.

I’d recommend you set up archiving first (I have it archive to year then year-month, but what works for you may differ), then Ctrl+A to select all your messages and click the Archive button. This’ll make the archive a bit more manageable.

Then you simply take the backup to another machine and do Tools > Import. All your messages will be imported, and you’ll have a well-organised history complete with full-text search on both machines. :)