What’s the most minimal way in which a page can be hooked into WP?

The template_redirect hook might be what you are looking for.

function template_redir_wpse_97289($content) {
  // code or file include, for example
}
add_filter('template_redirect','template_redir_wpse_97289',1);

That will fire just before the page template is loaded so you could use it to load your own templates.