Help with 'public' private server

Yes, this is my first post and yes, I am a complete noob at private servers, which is why I need help.

I'm trying to make a private server, and there are plenty of tutorials for that, however every one of them is centered around the idea that the computer they are on will be hosting the game (i.e. localhost). I have a virtual dedicated server I want to host the game on, not my own computer. Does anybody have a tutorial for this kind of setup? Something more than just "change the ip from 127.0.0.1 to whatever the server is" would be greatly appreciated.

Main questions are:
Do I need all the mySQL software installed on the server if it already has its own mySQL built in?
Do I run the 'StartGS' and 'StartLS' on my own computer or do I transfer everything to the server and run it via remote desktop connection or similar?

Thanks in advance for any help =)