Hi Gary,
It appears that you are doing what I did about two years ago - moved from a GoDaddy hosted environment to a GoDaddy Virtual Dedicated Server (VDS) environment.
It was a little bit of a learning curve for me, because I had to brush up on UNIX commands. I was quite worried too. But the move went fine. I am still not an expert at these things, but my site has been running fine on the VDS for two to three years. The biggest difference is that on the VDS, you have to do almost everything yourself.
Do you have Moodle up and running on the VDS already? If so, your config.php file might be fine. In my config.php file, my references are to my domain name, not my IP address.
You should think about backing up your site from time to time. This includes your mySQL database, and the moodledata directory. You should also double check your permissions for your files.
I keep thinking like you do that something is bound to go wrong. I have had only one problem, and of course, GoDaddy (via check) first said it was something that I did. After persisting, it turned out to be something on the virtual server size, and they fixed the problem.
I have learned how to upgrade my Moodle in less than five minutes, so my "downtime" has been almost non-existent. I too run a small site (12 courses a year, maybe 150 students or so per year).
Hope that some of this helps you.