I have motion sickness too. No Star Tours, Body Wars, Tea Cups and Mission Space is completely out of the question. I get sick in cars if I can't see out the window straight ahead.
We took a 3 day ferry to Alaska when my husband was stationed there. At one point we crossed open water (very rough) and I threw up for about 2 hours.
Our first cruise was about 6 months after that and I was rather worried.
The ships are just huge though. They don't move like rides and small ships. There is usually some movement the first night when you cross the gulf stream, and after that you will barely notice you're moving.
I take non drowsy dramamine every day as a precaution and I have never thrown up on a ship. On our Mediterranean cruise we had one day where the waves were approaching 20 feet (that's very rare) and I did have to lay down. But I slept through it and was fine.
I can't promise you won't get sick, but I can tell you the odds are you won't have any problems.