Yes, there are a number of service areas along the route where you can stop for a coffee or to stretch your legs. There are also public restrooms.
The trip from Rome to Positano or Amalfi can be stressful and exhausting. Consider that it will take at least five hours from the time you touch down at the Rome airport to reach the coast, and only if you're lucky with connections and traffic.
From Rome's Fiumicino Airport, you need to take the Leonardo Express airport train to the central Termini train station downtown Rome. From here, you need to connect to a train to Naples, and then a second local train from Naples to Sorrento, where you will hop on a bus to Positano/Amalfi. Or, you can take the train from Rome to Salerno, and then a ferry back up the coastline to one of the towns on the Amalfi Coast (this ferry line only runs in summer and routes are canceled in case of rough seas).
The numerous connections make it hard to purchase tickets in advance, because any delay could cause a domino effect of missed trains (the least expensive tickets to not allow for changes or refunds). Tickets for the train to Sorrento and bus to the Amalfi Coast cannot be purchased online in advance.
Trains from Naples to Sorrento are always overcrowded and do not have space to store luggage, so you will probably have to stand with your bags for most of the ride (about 70 minutes). Even the buses from Sorrento to Amalfi and Positano are often stuffed with passengers, so you may not find a seat.
If your flight gets in late in the afternoon or evening, your only option is to book a private transfer or stay overnight in Rome or Naples and head to the Amalfi Coast in the morning.
The cost and time of a public transfer: Eur60/person (adding together all the various tickets) and about 5-7 hours between Rome and the Amalfi Coast.
A private transfer will pick you up with a sedan or minivan directly at the airport or train station and your driver will take you and your luggage directly to the entrance to your hotel. The cost and time of a private transfer: Eur500/vehicle and about 3-4 hours between Rome and the Amalfi Coast.
If you plan on visiting Pompeii while vacationing on the Amalfi Coast, opt for a private transfer that includes a stop at the ruins along the way. It's a perfect way to make the most of your time!
Yes, there are a number of service areas along the route where you can stop for a coffee or to stretch your legs. There are also public restrooms.