Having just returned from an excellent cruise round the Caribbean on "Boudicca" I am able to answer your question regarding dress code. There were three formal nights where a Dinner jacket is worn. However there were numerous guests who wore a dark suit and tie without any problems. The dress code only applies to certain restaurants, I found that I took far to many clothes, I seldom wore a jacket, other than formal nights!! Smart casual is most suitable,short sleeved shirts, lightweight trousers and shoes (many wore sandals) for shore trips and to and from the onboard pools.
Rain is not uncommon at this time of year, take with you a lightweight plastic raincoat, I did not and got soaked to the skin. For the ladies, much the same in clothing, my wife took lightweight slacks and tops, something posh for the formal nights of course.
You will find "Boudicca" a wonderful ship on which to cruise the tropics, of all the ships we have cruised on she is the best by far, we will be going again next year. So I hope this answers some of your questions and I hope you enjoy your cruise in the sun as much as we did.
The detailed dress code will be sent to you with your documentation. However, the normal code is two formal nights per week (men in dinner jackets) and the rest a mixture of informal (men wear ties, jacket) or casual (almost always when in port) and on the first and last nights. Added to this, there will be "theme" nights eg Tropical, Western, Red/White/Blue. hope this helps.
Formal nights can also be a dark suit, you don't have to have a DJ.