Add default content to post (for specific category)

default_content runs when a post is loaded into the editor, actually. You can check for categories when the post is saved, but you’d want the save_post hook, probably. You want to check the $_REQUEST global.

add_filter( 'default_content', 'my_editor_content' );
function my_editor_content( $content ) {
  global $_REQUEST;
  if (isset($_REQUEST['post_category']) && in_array($some_category_id,$_REQUEST['post_category'])) {
    $content = "My html content.";
  }
  return $content;
}

… assuming no syntax errors. 🙂

You probably also want to check if the post_content is empty and insert only it is.