The shipboard experience will be similar to the Caribbean - except that you will be spending more time in port to actually see Europe. Lots of shore tours will be offered. The currency throughout Europe is the Euro - and the exchange rate vs the dollar is now very unfavorable. The good news is that you are on a cruise so you have already pre-paid for your lodging and meals, so seeing Europe won't be as expensive for you as it is for people who are not on ships.
Don't worry about getting Euros ahead of time, you can use your ATM card in the airport when you arrive. They won't take dollars there (they used to when the exchange rate was more favorable).
Expect the dress codes to be the same as the Caribbean - probably 3 formal nights on an 11-day cruise. Shorts & polos acceptable during the day (it will be hot in the Med in summer).
Have a great cruise!