Create menu with paths

In most cases, if a user doesn't have privileges for a path, they won't see the menu item either.

Oh, wait. You have a custom module? Did menu callbacks in the module not work? The Admin menu is automated, so to put it in the Admin menu, you'll probably have to inject it via the menu API.

I am writing a custom module and therefore, I want the creation of this menu to be programmatic rather than through the admin UI.

I am creating a custom content type that I want to, for convenience, be under its own menu cluster.

Say for the sake of argument that my module is named "Foo" and creates a content type "bar":

I want to create a menu at 'admin/foo' ( that is named 'Foo')

and I want to put crud under it:
'admin/foo/new_bar' (reading 'Create Bar') should be equivalent to '/node/add/bar'. However if I set its path to '/node/add/blog' it won't appear under the foo menu.

There are two conceptual ways to do this but I don't know how to execute them in Drupal:

1) create a page callback function that in turn routes the control to node add, telling it that I want to create content of type 'bar'.
2) somehow map 'admin/foo/new_bar' to '/node/add/bar' in the menu configuration.

Again: yes I can do this in menu admin but I need to do it in module code/config.