When we went on our first cruise, I too was very nervous. I don't like spinny rides at the amusement parks and I associated that nausea with sea sickness, which I've had when I was 10 or so. I never took a single pill! The designs of these ships is so advanced that there are times you won't even know you've left port. I work in the medical field and on several cruises I've talked to the staff and they too say that the number of sea sickness cases is almost nil. Enjoy your trip and put that idea aside.
Cruising is about doing as much as you want and as little as you want. Bring a good book, an extension cord and lots of adventure!