We need to review the networking ability of Unity first to see what it offers and how it offers it for us to use their built in features. Discuss with the team on the forum any information you find looking into this.
I would suggest using Unity forums, google, and working inside the project code trying the API out to test ideas.
As far as networking goes we want a server client application. So when a user sign in they talk to one server. Then when they play the game a console application on the server opens for that end user to share will all other players in that round. Once the round is over that console screen will report whatever data it needs back to the main server console application and then close. Wash, Rinse, and Repeat per game.