Where will I experience the least amount of motion on the ship?
Above: Calm seas in the Caribbean.
Below: The North Atlantic in a calm momemnt.
The short answer is in the middle of the ship as close to the waterline as possible.
Generally speaking, there are two types of motion on a ship. Sideways motion is called rolling. It is similar to the motion of a pendulum with the base of the pendulum in the middle of the ship at the waterline. The arc of a pendulum becomes less and less as you get closer to the base. Thus, cabins near the waterline will move less than cabins on the upper decks when a ship is rolling.
Ships can also move like a seesaw with the front going up and the stern going down and vice versa. This is called pitching. Just as on a seesaw, the place that moves the least is in the center.
It follows that the ideal stateroom if one is concerned about the motion of the ship is an inside cabin on one of the lower decks. A look at almost any cruise brochure will show you that these are the least expensive cabins on the ship. In contrast, the cabins that are most likely to feel the motion (i.e., those on the upper decks) are usually the most expensive cabins.
This underscores the fact that motion is not a significant problem for most people. Given the right weather conditions, any ship can move. However, it is usually less than the motion that one experiences on an airliner.
Of course, susceptibility to motion is very much an individual thing. I remember talking to one person who was in misery because of the motion of the ship. It did no good to point out to her that the ship was still in sunny Fort Lauderdale tied to the pier. Other people I have met like to book winter transatlantic crossings in hopes of experiencing once again the exhilaration of riding a ship through a great storm.
Cruise ship FAQs - - Motion and Stateroom Location