Basic "empty" entity type? Is there a module that provides an empty entity, to which I can add my own fields. I guess it would include just an Entity-ID as a primary field, and work with other entity modules.

For me, nodes have too much baggage included: title, nid, vid, publishing options, author and date.
You should really check out the Console project.
https://www.drupal.org/project/console

It allows for command line creation of modules, and will generate entities for your module. 

Here's a video explaining it all in 5 minutes.

https://www.youtube.com/watch?v=agcqTEr5_48

navigate to the modules directory in the drupal root in your command line tool 

enter command: bin/console generate:module enter the name for your module 

enter a machine name for your module hit enter for the default path 

enter a description hit enter for defaults for rest of questions 

enter command: bin/console generate:entity:content

enter the name of the module you just created 

enter a class name for the Entity you are creating