You are in for a treat, we have just returned from Bonaire, Grenada, Barbados, St Maarten, Tortola. In all of the places I would advise to do your own thing. There are any number of locals waiting for your business when you leave the ship (much cheaper than the ship excursions). Decide what you want to do, ie island trip, and then to a beach or shopping, bargain a price and then ask them to pick you up for return to the ship. Excellent island tours on grenada, tortola, barbados (call in for coffee at Sandy Lane hotel). Beach walkable in st maarten, exellent shopping straight off the ship in Aruba. Day wear shorts t shirt etc., etc., evenings cocktail dress and suit/dinner jacket on formal nights, smart wear on other nights, depending on what ship you are going on.
Aruba - try the submarine tour with Princess. Very popular and just been voted the best excursion by Princess customers for Aruba.
Bonaire - do your own thing. There is a hotel complex 45 minute walk from the port (along the promenade) where there is great snorkelling.
La Guaira - ship stops here because the fuel is cheap. AVOID VERY UNSAFE unless on a Princess excursion.
Grenada - RIVER TUBING!!!! (PRINCESS EXCURSION)
Barbados - Catamaran snorkelling with lunch. We did a shorter version of this and we really did swim amongst wild turtles as well as a ship wreck. (PRINCESS EXCURSION)
Antigua - do your own thing - go to a beach or Nelson's dockyard. Avoid Dickinson's Bay like the plague. Noisy and crowded.
St Maarten - the water really is blue!!! Good for shopping. Catch the water taxi from the port as everyone does. Fast and cheap. Can use several times a day with no extra cost. Beach at the town is fab.
A lot of these are Princess excursions. Some people find them expensive but it depends what you are doing. If it is sight-seeing, shopping or a beach it will be cheaper doing your own thing (plenty of taxis available). However such excursions like river tubing, the submarine tour, snorkelling with wild turtles are better booked through Princess. You don't have the hassle of finding companies that provide these tours and you have the added insurance that you'll always be back in time with the ship. Besides, it's good to mingle with others on the ship.
Clothing - Wear what you like! The dress code is no different to most 4/5 star hotels. In the evenings I wore smart clothing - trousers/skirt/dress with a smartish top. On 14 night cruises there will be 3 formal nights. Men mostly wear tuxedos or jacket and tie and women wear dresses or skirt/trouser suits - NOT the big fancy cocktail dresses! You don't have to dress up for every formal night but unless you are smart you will not be allowed in the dining room. We missed one formal night and ate in Horizon Court instead.