Restricted subreddit means that only approved users can post, but anyone can view. Private means that only approved users can view.

Another option is to set all posts by non-approved users to be automatically flagged (hidden to non-moderators), and moderators can un-flag the posts. Which, I think, is the workflow you're looking for? All you have to do is set the spam filter to "All" in the subreddit settings.

You still run into the problem that a lot of people might not want to use reddit, and you'll just end up fragmenting the people following your blog and lose a lot of readers.