As a rule cruising is a lot easier for people who may suffer from travel/motion sickness. I myself suffer from Travel sickness and have cruised a number of times. I recommend you visit your GP before you go and ask for the injection to help prevent Travel sickness.
A ship is a bit more stable than a boat of course, but you'll still get a certain amount of movement. I suffer from sea sickness myself but there are plenty of over the counter medicines that cure it. Ask your doctor or pharmacist. You need to start taking them before you board, because if you wait until you feel ill it'll be too late. Think 'prevention' instead of cure. Otherwise, you can normally get a jab on board, but this can be costly, and the tablets they give out at the purser's desk will just zonk you out. So the message is: sort it out before you go. Good luck.