Hi Terry,
I would use Joomlapack 2.1 (Joomla 1.5 although they do have a version for 1.0.x) as this will create a complete site back-up that can then be installed on a new server with minimum of fuss.
All you do is load the Joomlapack component. Configure to create a full back up. Download back up. Create new database and user on new host server. Upload the backup file. Upload the Kickstart file. Run Kickstart. complete the blank fields with new details.
Should all be up and running in under an hour
Hope this helps.
David