Backup and restore

I have done this many times and it is really as simple as you described. Two additional things though.

1. Did you also bring across the moodledata directory and reset it's directory permissions?

2. I usually open up the sql export in a text editor to do a 'find and replace' of the url. Moodle hardcodes links to images in posts and such, so these need to be updated to whatever your new url on the new server will be. Won't stop things working if not done, but will get rid of broken images yo would typically get after the move.

JR