How much time do you need when coming from the States to Rome, if you've booked a connecting trip to Palermo, Sicily on a discount airline like Ryanair? Do you have to pick up your luggage and recheck it?
If you are arriving from outside of Europe, you will need to go through immigration, grab your luggage if you have checked any, check-in with Ryanair, go through security and then get to your gate. If you are already in Europe, you will not have to go through immigration again but will have to pick up any checked luggage, check-in with Ryanair and go through security. Someone else with greater expertise on FCO can give you much better advice on how long to give yourself but I personally would want at least three to four hours to factor in a late arriving flight or long immigration/security lines.
Sept 2024 we had 3 1/2 hr layover in Rome before an ITA flight to Palermo. That was way more than needed. We were traveling all carry on. PS: we had no issues with ATI going into Palermo and out of Catania. Enjoy
If you are arriving from the States with checked baggage, note that it's a long walk to immigration and then on to baggage claim. As noted above, you would then need to check in and go through security before going to the gate for the flight to Palermo. The good news is that on a long layover you'd have numerous options for grabbing a meal.
You can start monitoring the on-time performance of your arriving flight to get a comfort level for the amount of time available for your layover.