I would just wait until you get to the train station and buy your tickets then. Sometimes Trenitalia runs some special offers, but sometimes the conditions for those offers are pretty limited. SO you could take a look at the website and see if searching for your dates offers a discount or not (it will say so).. if not, then I would personally wait. That way, you can take the next bus and then next train at whatever time you arrive without being stressed out because of time and timetables that need to be met. You're coming in September, but the airlines and airports are a mess, with many delays (and lost luggage along the way), so I'd just plan for worst case scenario and that you do get delayed and then would miss a train. This way, just go with the flow! ;-) As for the car rental company, if you arrive an hour late (or early) for pick up, they never make a big deal but you definitely don't ant to stress about the train beforehand.