Your Sail & Sign onboard account must be secured with a Credit Card or Cash Deposit. It is for all spending on board the ship.
The Casino does take cash, and quiet frequently from me
But you can get chips and tokens or cash there and charge it to your S & S account, there is a 3% fee.
I like many others use the $100 a day rule, I take $100 in cash/TC for each day. I secure my account with a credit card. I keep my Casino money seperate from that.
You do have the auto tips on your account, and if you drink it can add up. I almost always have money left and can pay down the account with it.
For Montego Bay, definetly take a shore excursion according to what I have heard.
Grand Cayman has great excursions, including Stingray City, and many others. It is pretty safe to walk around there without hassle.
Cozumel can easily be done by a first timer without an excursion. Unless you want to dive or snorkel offshore. You can get a taxi downtown for shopping, or to one of the beaches. I am now reccomending Paradise Beach, and they have an Offshore snorkel trip that leaves from there for $35 to Palancar Reef all equipment included. It leaves at 11:30 EST or 12:30 CST.
Hope this helps and does not add to your confusion. You will have a wonderful time!
Best wishes for a Fantastic Cruise