As the others have stated cruise money varies.
Based upon a budget, plans or needs everyone does things differently.
I can tell you I have changed over the years the way I handle money. Started out always using travelers checks, very little cash.
The moved to mostly cash with a credit card back-up. Now I primarily use my credit card.
But, as others mentioned bring small bills for tipping, taxis, etc.
It is possible to spend very little cash & have your shipboard account go to your credit card. While if you need to watch your spending then you can pay cash.
If you do not shop or drink your expenses will be little.
The standard tipping with Princess is $10 per person per day for the cruise. This goes to your ship account. Of course you can choose to eliminate this option & do tipping on your own.
Do hope you have a wonderful cruise.