Can't set Noce Access correctly for anonymous visitors

My problem: I want to create an intranet, using Drupal 7. Access should be limited to verified users.
So at first I turned off the 'view published content' for anonymous users.

But I also want a custom node to be displayed if that's the case, so then Drupal 7 contradicts itself...

So I installed Node Access and made an extra content-type.
The extra content-type is called 'general-errors' and can be viewed by anonymous users.
The regular page content-type I've set to only be visible to verified users.

Then, one of those regular pages I've set as the default front page of my website.
And a page of the 'general-errors' type I've set as the 403 node of my website.

So if a user is logged in, he should get the regular page, if not he should get the custom page.

Reality check: everyone (either logged in or not) gets the regular page. How come? :s

And another small question: since I have added this custom content type, each time I click Add Content it adds content from this type. Why can't I choose what type it should be?