The 12.42 train departure requires only two changes, at Chiavari and Napoli Centrale, but isn't very fast. From Rapallo (four miles away by expensive taxi) there is one option with only the one change in Naples, and a couple of faster options with two changes.
All other train options require three changes (or more). Travel by air also requires three changes - train to bus to plane to bus. Best will depend on your own criteria for price, speed and comfort which will depend on what date you are booking and the departure time chosen.
Thanks for the information. I now have options. The trip isn't until mid October so I have time.
Thanks for the information. It sounds the most practical suggestion so far.