The first night is never formal. Some people's luggage may not show up until almost dinner time, so it just wouldn't work. Usually the second night is the formal night.
As for the Captain's reception (it is not a Ball in the classical sense), everyone can go to it. Depending on the ship, there may even be two receptions - one for each dinner seating. Sometimes they are combined with one reception that can accomodate both seatings. The Captain and/or Hotel Manager will be at the door to glad hand the passengers and pose for photographs by the ship's photo staff. The ship's orchestra will play, waiters will circulate with trays of assorted cocktails and canapes, and then the Cruise Director will mount the stage and introduce the Captain. The Captain will then say a few words and probably introduce his senior officers. And then it is pretty much over. Figure 45 minutes or so.