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When you move your files to the new server, you will have to set the permissions again for template_c, uploads and cache (same as you would on a fresh install, check original documentation for details I've missed)
You will also have to edit mainfile.php to reflect the proper directory structure of your new host. Once you open it up, the changes should be fairly obvious, just use your old host information as a reference and change appropriately. It will also have to be CHMOD 444 after you make your changes.
As for your mySQL DB, export the tables from your old host and import into new host via phpMyAdmin. Another solution is to do a fresh install on your server to re-create the DB, then move your files over and overwrite your DB tables with your old one (assuming you kept the xoops_ table prefix). Keep in mind that you may have to tweak some permissions here and there.
Update your DNS entries with your registrar and allow a few days for proper propagation.(Im sure you know this already) Your new host will give you the NS details upon account setup if they havn't already.
This is just a basic rundown of what will need to be done for successful transfer to your new host. It's usually a painless process if you take your time and take things one step at a time.
Good Luck on the move