Hi hilo82, welcome to Cruise Reviews! Congratulations on your upcoming wedding, honeymoon and cruise! You cannot bring your own alcohol except for 1 bottle of wine per person. They will confiscate any alcohol you try to sneak on board and can actually deny boarding.
The additional money depends largely on what you want to do. You will be asked to either put up a cash deposit or a credit card and will be issued a ship card. This acts as your credit card and room key. So, if you put up a credit card, you can only spend the amount of credit you have on your card. If you use a debit card, they will put a hold on your bank account for a certain amount of money. The amount depends on the length of the cruise. You use your ship card for all on board purchases. These are for items not included in the cruise, which are: sodas, alcoholic beverages, items in the shops, extra fee restaurants (the main dining room is included in your cruise fare), any excursions you book on board, photographs, casino, and tips. They add gratuity to your bar purchases and will add tips for the crew to your ship board account. We usually figure $100/pp, excluding the casino.
If you'll look through our Europe Port Chat section a little further down on the main page, you will find posts about your ports of call. In the FAQ section there is a great article written by one of our moderators about travel in Rome.
The Solstice is a beautiful ship and I think you'll have a marvelous honeymoon, one that is certainly going to be remembered! Best wishes!