The plan as I would try it would be to take train from Naples with 2
large suit cases and 1 medium. Then walk or taxi to hotel in Sorento
to hotel. Then the next 2 or 3 or 4 days would be taking day trips
around the coast to the south east and then back to Sorento.
The easiest option with your luggage is the Curreri Viaggi bus from the airport that Kate was linked. Your bags go under the bus. Hopefully the schedule works out.
And be sure to book a hotel close to station. Taxis in Sorrento are fickle and expensive.
Second best is hire a driver 100-150euros- door to door.
Those are really the only 2 options I would consider in your situation. (Do you mean 2 large suitcases total or 2 large each??)
Honestly there is no need to travel along the AC more than 1 day, 2 at most. No reason you can’t see 2-3 villages a day (these are tiny, not cities at all)
Positano is all steep steps, high end shops and tiny lanes packed with tourists. Worth an hour or so.
Amalfi is a bit larger, the Duomo is worth a peek. Could spend 2-3 hours here. It will still be crowded in October.
Have lunch unless you head up to Ravello
Ravello is worth a few hours- allow time to walk out to Villa Cimbrone.
All 3 can be seen in one long day.
I would never want to make the drive around/along AC more than once in a stay in Sorrento.
Take a look at Mondo Guide tours- they have an AC drive that is well reviewed and affordable.
Or hire a driver that will make the stops you choose.
Or plan to rely on the ferry and bus for day trips.
If you have 4 nights- that is just 3 full days- 1 day for AC, 1 day for Capri, 1 for Pompeii or Sorrento? Evenings in Sorrento.
Sorrento itself is worth a day to just chill, enjoy views, eat well.
If you have more time- consider splitting your time- maybe 3 in Sorrento, 2 or 3 in Amalfi (transportation hub) or Salerno.
What time do you have to be at NAP for your flight? I would hire a driver for this transit. No question.
We spent 9 nights in the area our first visit- 4 Sorrento, 3 Amalfi, 2 Salerno.
It’s a chaotic area to be moving around in and only getting worse but if you want to see the AC then try to add as many nights as you can and really have time to see enough and enjoy. Might be your only visit there!