Lucky you! We've been on over 15 cruises and loved every one. As far as attire for formal night, almost anything goes, from nice pantsuit/dress to formal sparkly-all-over. We aren't "dress-up" people, so usually just wear what I consider Sunday church clothes, maybe with a jacket with some bling.
For excursions, we only go our own way if we know the island and know exactly what we want to do. Safety factor and punctuality factor as noted above. Beach excursions usually take you to a nice resort with amenities. On your own, you are limited to public areas that may/may not have amenities. We decide between beach, water activities like snorkeling, land sight-seeing (make sure the vehicle is air-cond and comfortable), and shopping on each island. Sometimes a combination. Each of these 4 islands have walk-to shopping at the port.
On board, be as active or lazy as you want. Learn a little about each island before you go. We put our tips on our ship account; drink tips are added to each drink purchase. We inform our credit card company that we will be out of the country so they won't question any charges we make. Be aware most cc's charge a foreign transaction fee. Last tip--you will have to pick up your bags to go thru customs. There are hundreds of black/gray bags, so put something distinctive on yours--like neon ribbons--to make it easy to locate them.
Bon voyage!