Will you have a car?
I like route #1, perhaps with some adjustments, based on what you want to do in each place.
First, are you arriving in Palermo from elsewhere in Europe, or from the US/Canada? Second, what time is your flight from Catania airport? Can you get there from Taormina in time?
As to your distribution of time, you don't have much. Cefalu is an hour by train from Palermo, if you can squeeze that in. if you need to recover from jet lag, I would suggest going directly to Cefalu and spending your first night there, rather than try to hit the ground running in Palermo.
I would consider making Trapani (are you going specifically to see Erice, or something else? Segesta?) a stop on the way to Agrigento, and give Agrigento two nights. The archeological zone is very large, and the museum is good, you would have a very full day just seeing those things. The city itself is very pleasant, lots of good restaurants and shopping.
Ragusa could be a daytrip from Siracusa (I would put the Ragusa night there, in Ortigia). Again, the archeological zone and museum (one of the best) will take an entire day, not to mention just walking around Ortigia itself. There is a daily market and a convenient parking area in Ortigia (if you have a car).
I have visited all the places you list by public transportation, be aware that schedules vary on weekends and some bus service between cities is either non-existent or very inconvenient on Sundays.
