The only cruise I have been on was on our 45th anniversary 3 years ago. We flew to Los Angeles and then to Honolulu where we boarded the Norwegian cruise ship, Pride of America and cruised from island to island. That cruise was "freestyle" so there were no formal requirements. The ship had 4 nice restaurants and 2 large dining rooms, so we had our choice of where we wanted to eat and what kind of food we wanted We did dress up for a special dinner in one of the nicer restuurants on our anniversary. Different cruise lines have different dress codes. Your travel agent should be able to tell you. You will love cruising. Enjoy!
The only thing I would do differently is not book so many day trips at port stops. We had a day trip every day except the last day (7 day cruise) and we were exhausted. They also had a lot of daily activities on the ship that we missed because we left the ship early in the morning and returned in time for dinner in the evening. (and the onboard activities were included in the price of the cruise---the day trips were extra.
Norma