Should I use the theme layer or a module to create a complex, static page?
The "Drupal way" would be to NOT create a module to hold content, and NOT create a module for a specific page(s). "Drupal way" would likely be to (1) put all of the language/content w/markup into a node, (2) put other outside-of-content markup and styles into *.tpl.php files and css files, (3) put any PHP functionality that isn't available already in contrib into a custom module, and (4) NOT put any content/language into a theme or into a module.