Just a word of warning. It can be very decieving whilst out at sea with a sea breeze. You will burn much more quickly than you think.
Any high factor eg 25 - 30+ and try to book tours departing very early morning to avoid mid day heat.
Oooh and wear a hat with a wide rim to protect your neck.
Wouldn't like to recommend a particular sun block, but don't think you need to take lots of soft drinks with you as most tend to be available 'on tap' in buffet restaurant during the day, although don't know about NCL especially. You've got to watch not make your luggage too heavy for the handlers. Maybe a couple of the cups with lids would be easier to transport and you could keep them topped up. Have seen lots of people doing it!! We only take big bottles of water for boiling / filling up water bottles to take on tours and buy at each port.
Banana Boat sun block is brilliant. I always use it for my kids and you can get it as high as 50 factor. But 30 should do. I would also recommend their Aloe Vera Soothing Gel.
As a family which has fair skin, skin which tans quite easily, sensitive skin and a few conditions in between, I find Boots Soltan sensitive range great and covers all[literally]. I am a high factor gal so from the south coast to south east Asia, I take factors 25 to 50 and use accordingly.
ALWAYS apply the factor 30+ sunblock before you venture outside. Wear a sun hat and, if you have to be in the sun between 11 am and 3 pm wear a t-shirt. Don't be tempted to join the 'seal colony' on the sunbeds all day! Remember tanned skin is damaged skin. Bottled water and soft drinks are readily available so you shouldn't need to carry them. Not silly questions at all, we have all had to have a first cruise at some time. Enjoy your holiday.
Try korres or burts bees which have up to factor 30 and are organic/natural so nasty chemicals to absorb into the skin.