In the back office on your blogs tab then permissions tab in the section for 'Can post/edit with following statuses:' only allow protected. All registered users will be able to see the post, but the internet in general won't - until the post is changed to published.

Yes, that's possible. Go to the backoffice, then Blogs tab. Choose the blog you want them to be able to post to, then choose permissions. Give them only 'Draft' permissions. Their submissions will show up when you click the edit tab and you can click 'Publish Now' to promote them to the main page.

That is exactly what I wanted.

Now, is there a way to make new users automatically draft only posters so I don't have to go into that permissions tab to set it to draft only? Or... do new users automatically only have draft permission?

New users don't have any permissions by default. You have to assign them. I don't know of any easy way to change that.

I've got this set up and it works great, but I've been unable to find a way either in the backoffice or in the code that sends a notification to my Privileged Bloggers (who have the rights to publish a draft post) when members of my Bloggers group (who only have rights to post in a Draft status) post something new.

Is there a way to do this? Right now my moderators check things daily, but it would be very convenient to have them notified that there are new posts to review.

Thanks!