which is the best way to customize nav-menu-template.php?

Simply add the following into your functions.php:

add_filters( 'nav_menu_item_id', 'wpse64308_nav_menu_item_id',10,3);
function wpse64308_nav_menu_item_id( $id, $item, $args){
    return 'menu-item-'.$item->title;
}