Currency US dollars all the way everyone understands them!
No, your luggage will have to be collected and taken through Customs in Miami. It is then usual for you to take it to use the Cruise Lines transfer bus and then to the hotel and your luggage goes with you.
The currency to use throughout the Caribbean is the US dollar but be careful when you are quoted a price that it is not a quote in the Island's own (dollar) currency as this can be half as valuable. Also that you change, when given, is in US cents and dollars. Enjoy Neil
You take your luggage from the carousel to the hotel, and then it travels with you on the bus to the ship the following day. I would suggest US$ for all the ports of call.
The hotel aspect of your question has already been answered, but with regards to currency I recommend you try and take a good supply of 1 (in particular), 5 and 10 US Dollar bills for tips and small purchases. If you have to give a $20 bill for a $1 purchase you could easily get ripped off or given dud notes in your change.
When you land in the airport collect your luggage and take it to the hotel with you. The following morning you will be asked to leave your luggage outside your hotel room and staff will collect it and take it to the coaches for you. This will be the last time you will see your bags till you board your brillant ship (your love it) then in a few hours your bags will be outside your cabin door for you.
The currency aspect Bradley is right, you will only need US Dollars but make sure you have small change the island shops will sometimes rip you off but if you only have large notes the customer service desk onboard the ship will change it for you. Have a great time .