2
That should work but all modules might not work properly
Try This.
BACKUP DATABASE - FIRST
Upload 2.0.5.1 to the new server, set folders to the correct permissions, copy all of the modules that YOU installed, NOT the modules that are part of XOOPS (the core),copy your old mainfile.php file to the new server, change the XOOPS_URL and XOOPS_ROOT_PATH to reflect the new server.
Try it out, it should work and this would be using your current (old) database. I just did this to see if it would work for me and it did, but all modules may not work properly because of some core changes between 2.0.3 and 2.0.5.1
This will be an easy way to tell you what will work and what modules you may have to update if any. DO NOT make any changes until you move it to your new database because that is your current Database and you don't want to mess it up.
Hope that helps.