You install the database as shared only if you want to make it available for multiple projects on the same server. See Using a Single Local Database Server for all Your Projects
Otherwise if you want just one project and a database just specify it in the project target options. This is preferred.
As you mentioned that you are on AWS EC2 instance make sure you run the server check from the context menu to make sure first all needed docker services are installed well. Also the server should run Ubuntu as this is what we support.
As we do not support AWS out of the box in resource manager, I would really suggest digital ocean or hetzner for much better and cheaper providers if you can choose.