Leonardo da Vinci–Fiumicino Airport: For Prati, take the Leonardo express to Roma Termini (about 32 minutes; roughly €18), then Metro A toward Battistini to Lepanto or Ottaviano–San Pietro–Musei Vaticani (about 8–10 minutes). It is not the cheapest route, but it is the least fraught with luggage. The cheaper FL1 regional train (about €8) is useful only if you are happy changing at Trastevere and navigating onward by tram/bus or taxi; it is not the clean Prati transfer. Avoid pre-booked “shared shuttles”: they are slower than the train and can cost as much as a real taxi.
Ciampino Airport: Take the airport bus to Anagnina, then Metro A toward Battistini to Ottaviano or Lepanto: allow 50–65 minutes and about €3 total. If you have late luggage or dislike changes, the Ciampino–Termini coach (around €6–7, typically 40–60 minutes depending on traffic) plus Metro A is simpler. A taxi only makes sense for a group or very late arrival; use the official airport rank, not anyone offering rides in the arrivals hall.
Roma Termini: Metro A toward Battistini is the obvious move: Lepanto is best for eastern/central Prati and Piazza Cavour; Ottaviano–San Pietro–Musei Vaticani for the Vatican end. Expect roughly 8–10 minutes on the train, plus station walking.
Roma Tiburtina: Take Metro B to Termini, then change to Metro A toward Battistini for Lepanto or Ottaviano. Budget 30–40 minutes including the transfer. A taxi can be sensible with several people, but in normal traffic it is not reliably faster.