Administrator verification for user role type
For the record, the option you refer to ("Visitors, but administrator approval is required") is not for all users.  It only applies to the Anonymous user role, and means that the Anonymous user is allowed to register at the site (gaining the Authenticated user role), but only after the administrator has approved the registration.

The "standard" way of doing this in Drupal is to set up the site so that the "Anonymous" user role does not get access to the content you want to reserve for verified users.

Then, to gain access the anonymous user must 1) register; and 2) the administrator must approve the registration (using the option you refer to).

How would this model work for your site?