I'm about to book my first cruise and I'm not sure which is the best part of the ship for the least movement - is the front, middle or back less affected by the action of the ocean?
Low and central. The center (midships) is least affected by pitching (boat rotating up and down when moving into/with waves), and low floors are least affected by rolling (boat rotating side to side when the waves comes in from the side).
Homework reading: https://en.wikipedia.org/wiki/Ship_motions
Most cruise ships have stabilizers that will keep the ship very stable in most "normal" weather, If you are very sensitive to motion it may feel unnatural to you because it makes for somewhat of an artificial motion (Roll on wave then pushed up by stabilizer (if they are active)the speeds are a little different). Overall unless you get motion sickness you will probably be ok anywhere unless you are sailing thru a storm.