Normally I would suggest an apartment, though unless it is a modern apartment, they can be a little cool / musty at that time of year. I'd go hotel instead - or a modern apartment like the one we stayed in in Pogerola.
If wanting to do Pompeii, Paestum & Herculaneum, I'd either be looking at staying in Amalfi to make logistics easier - OR - having a 2nd base, in the port city of Salerno, to use as an easy base for Paestum, Vietri sul mare (ceramics) and Cetara (seafood), but with the option of picking off Pompeii or Herculaneum from there via the easy train links. That then leaves the other week to explore the Amalfi coast itself, walking on the better days, taking the buses on the less pleasant ones.
There is one downside of the time of year, as much of the joy is of the incredible views of the coast, and as the daylight hours are reduced, so this great pleasure is curtailed. If the weather is really bad, it also compromises the wonderful and under-used paths, as the steps become slippy and need a modicum of respect at the best of times, but more focus and caution when wet. Still walkable for sure, however I'd probably take 10-20% longer when walking downhill (by way of illustration, there are ~ 1200 steps from Ravello down to Amalfi, each one could be a little slippy if wet, so good footing is important. On the flip side, cooler conditions make walking uphill more enjoyable!
Finally, normally I try to steer people away from driving, however at that time of year it becomes more feasible, but you still need calm confidence and a head for heights and good judgement of where the off-side wing mirror is. The car gives you much greater flexibility of where to base yourself, and avoids the constraints of public transport timetables. We'd still use public transport, but some people are more confident than us.
