Both trips take 20-30 minutes. Taxi takes about the same time to the center of Rome and costs about ITL50,000. Facility information found, again, at the Aeroporti di Roma website. The trips costs under USD10 in second class. The most convenient way to and from the port is by hired car or minivan.
Many companies provide such service.
One such is Limousine Service Rome . We have not used them, but have heard compliments from satisfied customers. Rates to and from the cruise port run under USD150. You could also hire a car, or arrange a car and driver for a day-long excursion. Just off-screen to the right of the red cross is the main station, Termini.