Some years back I set up my own Shiny Server to develop and test out different Shiny applications and libraries. This was a passion project where I got to build the server from a basic base image and work through the setup and implementation of apps, databases, service workers, authentication, and web servers. Many of the apps never really get finished, but for me the creation and problem solving aspect is the most enjoyable part. I stopped maintaining the project a while back and have since scrapped the server. The repo for the server can be found here
I used Digital Ocean to set everything up as its far less complicated than AWS/GCP/Azure and I've found they have very clear tutorials for a host of issues. Creating and maintaining the server was a great learning experience in itself and showed me the power of what a minimal cloud server can do. I ran DO's lowest power option for $5 a month which was plenty for hosting Shiny Server andRStudio Server as well as a couple of databases.