I'm looking for a module that will let me add every node of a content type as a link with a common parent link.
You can use Default Menu Link module for this and core menu settings for content type..
Provides the user with a check box on all content types to set the "provide a menu link" value to true by default.
This is basically a nice way to ensure the menu system is adhered to by all content authors.
You need to set Menu settings for content type..