There are some great papermaps (yes paper!) of Sicily you can buy and you can survive without a GPS. If you are driving in towns looking for certain specific locations GPS can be helpful. If you just need major areas or roads the papermaps and signs will be fine. Like much of Europe you need to know the town you are going to and the ones just before and just after as not every road junction lists everytown so you need a basic knowledge of the area you want to go if it is small. Bigger cities will not be a problem they are always labled.

Catania to Palermo without a car normally means bus and they are fairly cheap. The train means you have to go to Messina first so unless you want to view the "scenery" take the bus if you do not rent.
(There is no standard commercial flight between CTA and PMO)

If you do rent and are in it just for speed take the main highway but if you want to explore the south coast is nice, though the drive will take you a long time relative to what many from North America and some parts of Europe think of when considering distance and time.