The GameMode has a method, PostLogin, which will help you set up the player controller that was assigned to the new player. Remember that the server maintains true authority over the player controller so you can reference the active game state and update the player accordingly.
In order to spawn new game clients, at a later time, you’ll need to launch the standalone game. You could test this with 2 sessions. Fire up your server, change the color of the object. Fire up a client and the default object state should be different (matching the server).