Trigger a function after saving content type
There are some hooks you can use to do this, but they are all fired before the data is recorded in the database.

Have a look at hook_node_insert(), hook_node_update() and hook_node_presave(). The two first ones are fired only on insert or update, the last one every time.

After, another way to do so, is to add your own submit method on node_form, using the hook_form_FORM_ID_alter() (hook_form_node_form_alter()), which will be fired after the node is properly saved in the database.

If I were you, I would use a setting page for my module to set the content types to use.