Any suggestions on most reasonable transport from PMO to the Historic Center of Palermo?
The train from punta raisi station underneath the terminal to palermo centrale.
Or also the bus:
https://www.prestiaecomande.it/en/
Regarding the train, there are also intermediate stops you could use, depending on which is closer to your intended destination.
www.trenitalia.com
From Palermo Aeroporto Punta Raisi
To Palermo Centrale
There are many trains. If you click on the detail info it will show you all the intermediate stops too.
If you post your hotel location we can suggest the best station to get off.