A quiet compressor?

Don't box them in. Don't enclose them. Look at the compressor heads. They have cooling fins for a reason. If you box them in they get very hot, can damage the compressor and the electric motor (which gets very hot as well) and heat creates moisture. You don;t want that in your air lines.
That is why a metal shed works, you open the doors when you run it and close and lock when you want to store securely.