It works doing it as you are and what I usually did, copy over the files, upload the database, make the changes and you are off and running. However, I came across Akeeba Backup at http://www.akeebabackup.com/ and have been using it ever since. It basically backs everything up and you upload the zip file on the new server, extract it, and go to the directory and you will be directed to the installed and it will walk you right through it. Makes it a lot faster that moving everything over yourself.