Taormina to Palermo

My experience is limited only to using a car in Sicily. The drive from Taormina to Palermo is about 3 hours, all on a freeway. If you take the northern coast route (also all brand new freeway with lots of tunnels) it's slightly longer, but the town of Cefalu, along the way, is definitely worth a visit.
Traffic is very limited, except for when near Palermo (avoid arriving at commute time).
I'm not sure if you are going to PMO airport or to visit the city of Palermo. In any case having a car while visiting Palermo would be an expensive hassle because a car in Palermo is needed like a car is needed in Manhattan. Therefore if you decide to rent a car, return it to the rental agency upon arrival in the city and then visit Palermo without a car.

I'm hardly a "seasoned" Sicily traveler, having only been there once in April-May 2014, but the Autostrade in Sicily are so easy that even I would feel comfortable driving them. Except for the very beginning and very end of your route, Taormina to Palermo would all be on Autostrade. The smaller highways (Strade Statale and Strade Provinciale) were not as easy. My friend is an experienced driver and did just fine on these, but I would have had trouble.

My trip report, with some more details about our particular driving experience, is here: https://community.ricksteves.com/travel-forum/trip-reports/sicily-palermo-caltanisetta-siracusa-taormina

I did the trip by car almost 20 years ago with just a map and a wife who can't read maps. We had absolutely NO PROBLEMS. I'm sure the roads and signs are much better now, so don't worry. However, make sure you heed Roberto's warning about driving in Palermo. That was a nightmare. In fact, we drove around the entire island and had no problems anywhere except for Palermo (and some of the small town's narrow streets). Have fun! :)

I was just there last September, and there's a train from Taormina that goes through Messina and then on to Palermo. It was EASY! I bought the ticket at the travel agency in the center of Taormina (you can't miss it, there's only one) and the lady who owns it speaks perfect English. It was a Regionale train, it was inexpensive @EU20. The train was clean and on time. For God's sake, don't drive! FYI I was one of three 60 year old women traveling together. I think altogether it was only about 2 1/2 hours, and much much better than a bus!

I love Taormina and I've been there many times! This time we took a little vacation from our vacation and stopped in Cefalu and did a splurge hotel on the sea, Hotel le Calette and the views were positively jaw dropping! PM if you want more info.

Either bus or train appears to require one connection, which is not too difficult. Train schedules give you at least 30 minutes for the connection at Messina. I would not rent a car unless you want it for other destinations that are not served by bus and train. At http://www.interbus.it/Home.aspx, I see lots of bus departures for Taormina-Catania, then connections to Palermo are shown at http://www.saisautolinee.it/ricerca/index.asp.

Listen to me.........the TRAIN!!! It's cheap, it's fast. Take a look at a map of Sicily!!! Why would you take a slow bus South to Catania only to take another Slow bus North, going through traffic, winding roads, etc., when the train is so much more simple?The trains don't have to deal with traffic, go faster. The Travel Agency in Taormina is so EASY, I think you're over-thinking this, and I'm sorry, although I've used RS guidebooks/advice for years, but she's WRONG! (No offense) I just did this!!!