Creat new menu items link in menu like create new Content Type does
You do not need to use php code just to create a menu with menu links. You can do it with Drupal Core itself.

See below detailed tutorials that may help you.

How to create a menu and add links to it in Drupal 7

Advanced Drupal 7 menu settings, how to create parent child menu links

Create Drop Down Menus in Drupal 7 Using Nice Menus module

If you want to do it specifically using Custom Code then your callback function should call drupal_goto with link as an argument.