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.

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.

Edit: Chip's answer makes more sense and he clearly has more experience than I do.