Normally, you would use the built in user group if you wanted to change permissions for new users, and have a other user groups for when you need to change that (i.e. adding or removing rights). That would be much more straightforward, easier to maintain, and easier to understand for other administrators of your wiki.
If you really need to add every new user to another user group (you don't tell us why this would be necessary) you can use wgAutopromote
, as pointed out in the comments:
$wgAutopromote = array(
'myUserGroup' => array( APCOND_EDITCOUNT, 0 )
);
Also, note that you can't directly remove a user from an autopromotion group through Special:UserRights.
Edit: As per the comments I understand that the unusual solution you are suggesting in your question is actually not needed. You should just create a user group for user that are not supposed to access the internal documents (e.g. $wgGroupPermissions['InternalDocs']['restrictedusers'] = false;
), and then configure your extension to prevent them from accessing some documents. You might want to consider a better maintained extension for than the one you are using, btw, see: Editing permissions of MediaWiki default namespaces
Also, be adviced that MediaWiki is designed for openess, and any attempt to circumvent that, will have holes. See https://www.mediawiki.org/wiki/Security_issues_with_authorization_extensions