Flight recommendations for Sicily

I start with Google flights, sort for number of stops (one or less--will def be at least one stop for Sicily). Just doing a dummy flight without dates, I see Turkish airlines is on there. If you don't mind the long layover in IST (I would), it's probably going to be a good deal price-wise.
If you have time for a stop over, flying direct to a major city and then changing to a different airline (you need ample time between to do it this way) is also an economical.
"Easiest" is booking through all the way on one airline, so I'd try that first and see what kinds of layover options you have to choose between--you appear to have one stop options on Swiss and United/Lufthansa (I would try to avoid Frankfurt airport based on some annoying experiences there).

We're doing the Sicily tour in April. Delta/KLM flight from O'Hare to Rome, with a plane change in Amsterdam. American has non-stop flights ORD-FCO, but our loyalty is with Delta and we're traveling on Skymiles. We've got a week on our own in Puglia, then are flying from Bari to Palermo on ITA. That itinerary involves a plane change in Rome. I just today booked the Bari to Palermo flight. I had a choice of layover times at FCO, since ITA has flights from Rome to Palermo throughout the day. On the day we're doing this, ITA's afternoon and evening flights from Rome to Palermo depart at 1:20 p.m., 3:20 p.m., 5:10 p.m., 8:05 p.m. and 10 p.m.

So you could book your international flights round trip to/from Rome's airport and then separately book Ryanair or ITA flights to get from Rome to Palermo, and on the other end of the tour, from Catania to Rome. To avoid missing our international flight home, we're leaving Catania on the last day of the tour, flying on ITA to Rome, staying overnight there one night, and doing the Delta international flight the next day. You could also build in that cushion on the front end of the tour, international flight to Rome followed by a Ryanair or ITA flight to Palermo the next day.

When are you traveling? ITA Airways will start nonstop service to Rome from ORD on April 7 - six days per week, and daily starting June 3 for the summer. From Rome they offer frequent connections to both Palermo and Catania - so you could book the trip on a single ticket.

I went there last here and flew through Frankfurt and from there had a direct flight to Palermo. It's a small airport so you will need to connect in a larger city within Europe and then take a second flgiht.

Thank you for the help on my flight plans. I guess there is no easy way to get there. Thank you again and Happy Holidays!

It depends who you prefer to fly with and time of the year you are flying. During the summer United had a direct flight into Palermo from Newark I believe. Please do some research. When we flew to Palermo before the pandemic we went through Munich which was an easy stress free connection