Opposite direction, port to FCO, we used Leader Car Service. Communicated thru WhatsApp and our driver was early and efficient. Used the toll road and the drive was maybe 40 minutes. Going to the port, we took the train, had carry on size only and book bags. Our AirBnB was walking distance to Termini and we had booked the intercity train pretty early, when the schedule opened; 29 euros for 2 first class tix. As an aside, try to pack with carry on only, even if you’re not using public transportation. Wear things 2-3 times, rinse if need be; you’ll be so much happier!