I'm afraid my question is a no-brainer for almost everybody, but I can't find the answer. I can't find it using Google, StackOverflow or by examaning the code generated by Features.
How can I store the default theme of a site in a feature? Do I need Strongarm? What would be the name of the variable?
(It feels like a duplicate of Drupal Features include Theme, but we're four years further now)
If you mean the actual theme, templates and all, then no. Features is only really intended for bundling configuration. If you just mean the setting for the default theme, yes: install Strongarm and select the theme_default variable when you're creating your Feature.