What’s the best way to customize the WordPress Menu Page (in admin)

Editing the the file is not a good idea, it’ll be replaced next time you update your wp installation, why don’t you just enqueue a new css file and overwrite what you want to change, a lot can be accomplished with css without changing the markup.

if ( is_admin() ) {
    wp_register_style( $handle, $src, $deps, $ver, $media );
    wp_enqueue_style( $handle );
}