Transportation from Rome, Italy to Pistoia, Italy

Are you arriving at the airport that day? There’s a fast train departing from ROMs Fiumicino Aeroporto railway station at 1:53p arriving in Florence at 4:11p meaning you would only change trains once to get to Pistoia. The train from Florence (Firenze) SM Novella station to Pistoia takes another 45m (six stops). Otherwise, you must take a train from the airport to Rome’s Termini station and transfer again in Florence: https://www.trenitalia.com/en.html.

I think the train to Pistoia would be your best option - if there are places you want to stop in between, you have a lot of options with the train.

We are actually spending three days in Rome before heading to Pistoia. We have a lot of flexibility on the day we leave for Pistoia. Is renting a car in Pistoia a good idea?

Is renting a car in Pistoia a good idea?

That depends on where you're going. If you don't rent a car you'll have to rely on the train, bus or taxi to get around. That's not a bad thing if all points of travel are direct. If connections are involved then you may want to rent a car.
One of the problems with renting a vehicle in IT is you need to read up on ZTL zone fines. A second or two in a bus lane or pulling into a spot along the side of the street can be costly. These fines can take up to six months to reach you and the amount of the fine goes up daily. It's not unusual to be fined around $300 for one of these. I'd hate for you to make that mistake twice.

Yikes! I guess if we rent a car, we should do it in Pistoia. We've been to Italy several times, and only rented a car once, and that was years ago so I am sure things have changed.