Members Site

I’m trying to make a members site with wordpress. The way this would work is I make a post, and make it privet. Then a member can log into their account, click view site, and see that privet post. People not logged in can’t see the post. I want the user to only be able to go to the page, and maybe comment if they want. They can not make a post themselves. If I make them a subscriber, then they can’t see the privet post!

Is there a plug in or code to make what I want?

Eric