There are two airports in Rome: Fiumicino (FCO), which is also referred to Rome’s Leonardo da Vinci Airport, and Ciampino (CIA).
Fiumicino is better since it is the main international airport with four terminals, where three of them are in the same building, while Terminal 5 is in another building and is for passengers coming from US and Israel. Airplanes from US, Canada and many other countries land only at Fiumicino. Also it closer to cruise port Civitavecchia.
Talking about Ciampino, it has 16 gates, in compare to Fiumicino’s 36, and all of them are in the same building. The airport is small, so don’t expect huge duty-free and a variety of restaurants.
Interesting fact: Ciampino is an old military airport which is now a base of budget airlines like RyanAir.