Start with the booking, not the number of connections
Catania–Fontanarossa Airport, code CTA, is the air gateway for this side of Sicily. A nonstop from New York gives travelers in the States a direct option. Otherwise a change in Rome or Milan, or at another European hub, can bring you into Catania.
The difference between those itineraries is not merely what happens between departure gates. It is who has to solve the problem if Catania stops accepting incoming aircraft. I want the connecting flights on the same booking so the airline has responsibility for getting me to the destination when its itinerary changes.
Separate bookings can make a connection look attractive on a search screen. They also turn the next flight into a new commitment rather than part of the same journey. If the inbound plane is diverted, you may reach Sicily without reaching the airport where your onward reservation expects you to be. A good-looking connection has now developed a taste for paperwork.
A booking site can display connecting flights together without making them a protected journey. Before paying, I would check whether the onward flight actually sits on the same reservation.

What an ash closure actually changes
When Etna sends ash into the air, Italy’s volcano institute, INGV, issues an aviation notice called a VONA. The alert is color-coded, with red at the top. The airport company SAC then restricts the airspace sector affected by the ash. The wind matters: a closure can halt arrivals while departures continue, or interrupt both.
A passenger may see a flight held while the airline waits for permission to operate. Another flight may be diverted to Palermo, Comiso or Trapani. Those airports have taken diverted traffic in recent seasons, and ash interruptions have recurred this year.
What would bother me is not being in the wrong Sicilian city for a while. It is having a nonrefundable departure, an onward long-haul booking on a separate reservation, or accommodation that cannot move when the flight does. Ash is outside an airline’s control, so cash compensation is unlikely, although the airline still owes care and rebooking.
Before leaving for the airport, check the flight with the airline and look at SAC’s updates. I would keep the arrival and departure nights flexible and read the volcanic-ash wording in the insurance policy. Some policies address it specifically.
The airport rail stop comes with a ticket catch
After landing at CTA, the bus into Catania is the straightforward option. AMTS runs the Alibus from the airport into the city and to Catania Centrale railway station. You can buy a ticket aboard. Taxis wait outside the terminal too, for anyone whose destination doesn’t suit the bus route.
Rail is a different arrangement. Catania Aeroporto Fontanarossa is a railway stop reached by a footpath from the airport, with an AMTS shuttle also linking it to arrivals. The station name makes the connection sound self-contained. The ticket does not necessarily agree.
When buying through Trenitalia, the destination labeled “Catania Aeroporto Fontanarossa” excludes the shuttle. The entry labeled “Catania Aeroporto Fontanarossa Bus” includes it. That extra word is doing genuine work. I would select the Bus version when I intend to use the shuttle, rather than discover the distinction after collecting my bag.

Eastern Sicily can begin without a stop in Catania
Landing at CTA does not mean the city has to be your base. Regional trains from Fontanarossa connect toward Siracusa, Taormina and Messina. Coaches also leave from the airport itself, which may remove the need to go into Catania and back out again.
Etna Trasporti connects the airport with Taormina and Giardini Naxos. Interbus serves Siracusa and Noto. A coach at the terminal and a train at the Fontanarossa stop are different departures, even when a booking search files both under the airport’s name.
I would make the choice from the place where I actually intend to stay. For Catania itself, the Alibus takes you toward the city and Catania Centrale. For Taormina or Siracusa, look at the direct coach and the regional train before adding Catania as an unnecessary intermediate stop.

Put the border check where it belongs
US citizens can visit Italy for short tourist stays without a visa under the Schengen rules. The part I would build into the flight connection is the Entry/Exit System, known as EES. It records a face photo and fingerprints at the Schengen border in place of the old passport-stamp routine.
If you change planes in Rome or Milan after arriving from the States, the border check happens there rather than in Catania. I’d leave room for those formalities instead of planning the layover as though the next aircraft were waiting just across the corridor.
ETIAS is not operating yet, so there is no authorization to apply for through that system today. A website pretending to sell it isn’t supplying a valid travel document.