we are considering flying from Genoa to Rome. How long before our flight should we plan on arriving?
It is fairly universal and similar to the US. I would plan on at least an hour and half and maybe two hours for a mid day departure.
It's a domestic flight so Alitalia requires that you have checked in and have a boarding pass 35 min prior to departure.
So get to the airport 60 to 75 min prior to departure and you will be fine.
However consider that the train is probably just as fast once you add the transfers to/from airports and the security checks and the deplaning.