Subscribing the new user to a mailing list as a part of registration What is the simplest way to configure Drupal in such a way, that every registering user is asked for his email and permission to send him  info about site updates?

That way I want to postpone serious site building, but have a solid user base just from the now.
The email address is already a standard user property. Using fields you can ask for permission about the mailing list.

You can use rules module (http://drupal.org/project/rules) to get notified of new registrations and find or implement the action for a mailing list registration.

Another option would be the simple news module: http://drupal.org/project/simplenews