Amalfi Coast from Rome

Trains go to Naples or Salerno.
http://www.trenitalia.com

From Naples Central Station you can reach Sorrento with the Circumvesuviana commuter train.
http://www.eavsrl.it/web/home

From Salerno and Sorrento you can reach the Amalfi Coast via bus.
http://www.positano.com/en/bus-schedule

There is also a bus from Roma Tiburtina station directly to Sorrento. It's with the Marozzi Company. It takes longer than the train, but I presume it's a comfortable ride.
http://www.marozzivt.it/home

Boats are available from Salerno to the Amalfi coast, but probably not when you go (summer only)

Hello Kim. I would recommend staying in Sorrento. I've stayed there twice before (and again this May) and love the home base of Sorrento. You can travel by bus to Amalfi, Positano, Ravello and Capri by ferry. I highly recommend staying with Antonio at Villa Elisa. Great location and very affordable.

1.) Best way for most is to take the train from Termini to Sorrento or Salerno. I say for most because if you are staying in Rome close to Termini it is best. I prefer the bus as I prefer to avoid Termini and also Naples train station and the bus allows for that. Have to take a taxi to get to the bus station in Rome but it brings you to Sorrento comfortably though definitely SLOWER than the train. The bus schedule is loosely followed where the train is generally on time.
I found with luggage this was the easier method of travel for us though, no steps, no crowds, no pickpockets, etc...
It drops you off right at the Sorrento bus station so either walk or taxi to your Sorrento hotel or board another bus from the same station to Positano or other town on the coast where you are staying.

2.) With 4 nights I would choose either Sorrento or Positano not 2 and 2. If you had 5 or 6 nights I like the idea of breaking up the stay better. I prefer Positano but Sorrento has some advantages, mainly logistics which can be a big one.

I plan to go to Naples and the Amalfi Coast around March 23-26. I'd like to see Pompeii and hike the Walk of the Gods or others. I can catch a Viator Pompeii/Vesuvius tour from Sorrento. All the warnings are about crowds in the summer, but how is March? If no boats are running, are the buses available? Do the Naples ferries run year-round? Will I be able to get around the peninsula? If it is raining, I may need to stick to lower hikes.

I plan to go to Naples and the Amalfi Coast around March 23-26. I'd like to see Pompeii and hike the Walk of the Gods or others. I can catch a Viator Pompeii/Vesuvius tour from Sorrento. All the warnings are about crowds in the summer, but how is March? If no boats are running, are the buses available? Do the Naples ferries run year-round? Will I be able to get around the peninsula? If it is raining, I may need to stick to lower hikes.
Joanne

Kim, it depends mostly on when you go. With 4 or even 5 nights, it's too time-consuming to change locations.

March is definitely off-season and you'll probably have to choose between Sorrento and Salerno. There is regular bus service for day trips to the AC towns. Most, if not all, of the attractive shops will be closed and many of the restaurants, but you'll have the views and the hikes (and maybe some cold winds). Salerno is easier from Rome because there are direct trains. However, there will be few tourists using the local Circumvesuviana train between Naples and Sorrento, so it's an easy transfer and you don't need to worry. I'd stay in Sorrento only if you want to visit Capri and/or Pompeii.

May is when the ferries start running and tourism really picks up. Expect all the hotels, shops, etc to be open and warmer weather too. You can take the bus to the top of the town and work your way down, then ferry back. Positano is said to be the most expensive, so you may want to stay in Amalfi or another town - or even less expensive Sorrento or even less expensive Salerno.

April is in the middle. No ferries yet, but maybe the tourist-oriented places are opening up.

Joanne - the only ferry service is to Capri, Ischia, Naples and Sorrento. You can get to Capri from Naples or Sorrento.

Chani, thank you for the reply. Good reassurance about bus travel. I know that March is off-season, but it is when I will be there, after a tour.

Joanne - I'll be there in February, couldn't manage it later. I think March will be better ☺