I have no experience with GoDaddy VPS, but it sounds like you get a VM/Machine that is your server, which is common with few hosting services out there.
The good thing is you can do whatever you want, the bad thing is choosing what. The easiest thing you usually can do is use git to clone your repository into the VPS machine, and setup everything from there. You have complete control over this sort of setup usually.
Alternate approaches could be installing some software to do some deployment management, either on the VPS or an external service.
The general idea is if you have a machine sitting in the corner of your room, how would you setup your application on it to run “in production”? That’s about the level of complexity your looking at. Your welcome to look up specific guides for your MERN stack, and how to manage one in production.
Goodluck 