Here you can find the official fixed prices applied by regular white taxi:
The train arrives (or leaves) directly to Termini Station (the main station of Rome) every 15/30 minutes,
you can find the timetable
The cost is € 14 per trip (adults can bring with no fee one kid under 12 and children under 4)
From the train station with 7 minutes walking you can reach RTS
The bus is the cheapest way to travel from an to the airport, around € 7,00 per trip.
There are three companies that ends their run in Giolitti street (the street that runs on the nearest side of Termini Station):
T.A.M. (just for Fiumicino airport), Terravision and Schiaffini (for both airports).
You can find the timetables here.
From Giolitti street with a walking of 5 minutes you'll arrive at RTS.