Beau, it is great that you know how to set up your own server, I admire your abilities.
Yes, I see GoDaddy calls these VPSs now, they used to be VDSs. Oh well.
I have the "Value" one, which I see is between $32 and $40 right now, depending on your commitment. Yes, I know what you mean about "bad mouth GoDaddy", and I too have not had any real problems with them. From the server side, they seem to know what they are doing. Can't expect them to know everything about every application. If you need this kind of knowledge, one would be better off with a Moodle partner, but your not at $50 per month.
Yes, a "Dedicated Server" is much more expensive. It will probably be a long time before I need one of these, especially since I have 3 more steps available with the VPSs.
Since you know the Linux stuff well, you might actually have some fun experimenting with one of the VPSs. You would probably be able to assess how well GoDaddy configures these things, then you could share what you learn will all of us. Also, if you start with one month, GoDaddy (as you probably know) will likely send you emails with bigger discounts on these VPSs.