We are going to Sicily in early November - our flight from the U.S. arrives Rome FCO at 9:10 a.m. How much of a time gap should we allow to pick up luggage/go through passport control, etc and make it to our new gate for the flight to Palermo? Also, which airline to Palermo would you recommend? It looks as though Alitalia, Ryanair and Vueling would be my options that time of year.

Thanks in advance-

Although we prefer Vueling to Ryanair, I think Ryanair has an 11:55 a.m. flight to Palermo. We thought RyanAir a little better than some past experiences when we flew them to Sardinia last fall. You should have plenty of time to make that one. The last time we were at FCO, we found some good food there, and if you have to wait, not a bad place to do it. We have had good experiences with Alitalia in the past, but they have been teetering on going out of business, with a possibility of Easy Jet taking them no longer in the mix.

What airline are you flying from the US to Rome?

If it is a partner of (or has an interline baggage agreement with) Alitalia then you can check your bag all the way through to Palermo.

J62 is pointing the way for you. There will be far less stress if you book a single itinerary from your departure airiport through to Palermo. There are about a dozen cheap flights from Rome on three airlines (I always use Skyscanner.com to find discount flights). But for many of them you will spend a couple of hours going through complete immigration and customs proceedings before moving to the second flight's departure and checking in as if you had spent a month in Rome. The other reason to not DIY is that the most convenient and economical way to get to Palermo might be through a different, non-Rome international gateway. Turning up all the possible alternatives for each leg is very hard on your own.
PS: If you do choose to use a budget airline into Palermo, the flight's about an hour, hardly enough time to 'enjoy' differences between the competing airlines.

The way i read the OP is that they have already purchased their US to FCO tickets, and now want to tag on flight to Palermo. It doesn't even need to be on one single itinerary, but flying same (or partner) airline, or at least one with an interline baggage agreement can greatly simplify the transit at FCO instead of having to exit clear out to the public area, re-checking in, etc. In my experience waiting to collect bags at FCO can be an interminable wait.

If the bags are checked through to Palermo then there is no need to go through customs at FCO, just immigration.

We have purchased our flights to Rome on American. How would I find out if American has a baggage shipping agreement like the one you described (I kind of doubt they do)?

"How would I find out if American...."

Call AA...

In recent years airlines have reduced the number of interline agreements (not shipping agreement) so it may be a long shot but worth a try. Vueling is owned by AA / Oneworld partners BA & Iberia so it may exist.