Assuming the "order" column is part of this same table, decide if you want to list in ascending(asc) or descending(desc) order and simply add 'ORDER BY order ASC'
$resultl = @mysql_query("select first_name, last_name, phone, email, category from directory, categories where department = categories.category_id and department= " . $row['category_id']."ORDER BY order ASC); //or DESC sort
Hope this helps