What are best practices for deploying an app to a VPS?

I am working on an MVP, which initially ran on Heroku to simplify things. However, I'm realizing I need to move to a provider that gives me control of the the server (likely AWS Lightsail since I'm already familiar).

What is the best practice for deploying applications to a VPS? I have found resources for git hooks, but those seem to focus on static websites. I would love to be able to run "git push prod master" and use git/scripts to automate building and deployment.

Do you have any good resources or recommendations for doing this?