Docker & Databases. Stack or Individual?

So I'm in the process of (re-) setting up my homelab and unsure about how to handle databases. Many images require a database, which the docker-compose usually provides inside the stack.

Now my question, shall I have 1 database container which is accessed by all containers? Or shall I have a separate container for each service?

For critical services, which shall have as few dependencies as possible I'm already using sqlite or a similar solution.

Also on a sidenote: I have two docker hosts, can I let the containers of 1 hypervisors use the same internal docker network?

TIA!