A rental car is the last thing you want if travelling the AC between April and October. Backed up traffic and a dearth of parking availability. Depending on where you will be staying, take a train to Naples or Salerno. Then by private car service (or ferry from Salerno). Location during your stay depends on what other places you want to visit. If only the AC towns, then Amalfi makes sense. But if you want to include days visiting Capri, Pompeii, and Naples, consider staying in Sorrento instead.
Travel between the AC towns can be attempted by bus, but be aware of possible long lines, SRO, or buses not stopping because they are already full. Otherwise, look at the ferries. Except Ravello, which can only be reached by bus or car.