Bring a credit card to register with the ship when you check in - almost ALL of your charges will be tabulated automatically during the cruise - the only cash you need is for possibly in the casino or on shore.
How much will it cost you? About $11/day per guest in gratuities, plus any special dining you may choose to pay for, souvenirs, transportation, etc.
In terms of cash I go on cruises where I use almost no cash at all, but it is good to have $100 in cash just in case you want a souvenir or to take a txi someplace.
On your charge account you may get a massage for about $120, order soda ($3.00 or so), maybe a specialty coffee (about $3.50) & things like that (but those things go on your onboard charge account, not cash).