Leonardo da Vinci–Fiumicino Airport: For Termini, take the Leonardo Express: non-stop, about 30 minutes, €14 each way. If your hotel is nearer Trastevere, Ostiense/Piramide or Tiburtina, use the cheaper regional FL1 train instead; it does not go to Termini and is roughly €8. Airport coaches can be cheap but are traffic-dependent, so they are a budget fallback, not the default. Official taxis have a fixed fare inside the Aurelian Walls; confirm the posted fare before leaving the rank.
Ciampino International Airport: Do not assume there is a rail station at the terminal. The sensible public-transport option is Trenitalia’s Ciampino AirLink: train from Termini to Ciampino station, then the connecting airport bus, about 40 minutes in total on one through ticket. Direct airport coaches to Termini take roughly 40 minutes but can be slowed badly by traffic; use one only when its departure is materially more convenient.
Roma Termini: This is the useful central rail arrival: it connects directly to Metro A and B, buses and taxi ranks. If staying in the historic centre, walking or taking a short official taxi is often better than wrestling luggage onto a crowded bus; for Vatican/Prati use Metro A, for Colosseo/Piramide/Tiburtina use Metro B.
Roma Tiburtina: A major high-speed and regional rail station, but not a destination in itself. Take Metro B toward the centre/Termini; allow about 15–25 minutes to central stops, plus the walk to your hotel. It is efficient for connections, less convenient than Termini for a first-time stay in the historic core.