1) Recommendations for car service from Naples to Ravello
2) Which town would be the best "home base" in the Amalfi area, where transportation is readily available to visit the various towns.
3) Is a day trip to Sicily doable from the Amalfi area?
1 - No idea, but as an alternative, take the Frecciarossa (train) to Salerno, bus to Amalfi (town) and then bus to Ravello. OR Circumvesuviana to Sorrento, bus to Amalfi (town) and bus to Ravello.
2 - Probably Amalfi is you are truly concentrating on the A.C. and not on Sorrento. You can easily bus (or ferrry?) to Positano, Praino, Ravello, etc. If you stay in Ravello -- which is lovely! -- you are a 30 minutes bus trip up from the seaside.
3 - Sicily, no. not feasible. Not a day trip sort of place even if the transport would work.
Amalfi is easiest for transportation links, or Positano.
Sicily as a daytrip is almost impossible - you would have to fly, and flight schedules are not daytrip friendly. As Laurel noted, Sicily deserves/requires more time.
You might consider a daytrip to Paestum.
Thank you Laurel and Zoe for your suggestions and advice.