It reads like you want a custom post type with supports only for post-formats.
$args = array(
...
'supports' => 'post-formats'
);
register_post_type('testimonials', $args);
http://codex.wordpress.org/Post_Formats#Adding_Post_Type_Support
You could create a custom archive for your post type by copying a regular archive page and naming it after your custom post type, such as archive-testimonials.php See Post Type Templates in the codex.