The train goes directly from Siracusa to Naples, with stops in Catania and Taormina. It also stops in Salerno, which is a convenient drop-off point for the Amalfi Coast. It's an 'Intercity' train that leaves Siracusa twice a day, in the morning (10:25AM) and in the evening (night train).
I strongly recommend dropping off the car in Siracusa and taking the day train. Driving into Catania will definitely not be worth it and I'm not sure why you are considering it. FYI, dropping off a car to meet this train is most easily done in Siracusa or in Taormina the night before (day train), with a taxi to the 'stazione' for the departure, IMO.
As a side note: daytrip into Catania from Siracusa, using the bus or train (or both). Don't take your car into downtown Catania. There's an Interbus stop right behind the Duomo, in Catania.
The train to Naples is a comfortable ride, in compartments of six (2nd class). There is no bar car or snacks, so pack your own. The scenery is nice and it's more relaxing than driving.
The really neat thing about this train is that it gets loaded onto a ferry. The locomotives stay on each side, so it's just the railcars that cross. For the crossing, you can leave the train and go above (make sure someone is keeping an eye on your bags!). I was on this train to/from Reggio Calabria earlier this week and took lots of photos!
I can highly recommend a taxi driver in Siracusa who is very reliable, honest to a fault, and who speaks English quite well. He's available for pick-ups and drop-offs within Siracusa and from/to Catania Airport. His name is Giuseppe Trupia, tel: +39 330 97 56 89. His e-mail is [email protected]
Thanks to him, I've made it to the 6AM train from Siracusa to Palermo a couple of times last month!