Train/rental car advice-Venice-CT-Florence-Rome

I would rent the car in La Spezia (next to the Cinque Terre) instead of Florence. From there I would drive to your Agriturismo. That would save you the trouble of taking 2 or 3 trains (with luggage and all) to Florence, then the taxi to the rental car location.

If you pick up on a Sunday (when the La Spezia rental offices are closed), then Pisa airport is the next best.

If you intend to return the car in Orvieto, instead of Rome, then Hertz is the only option available in Orvieto.

I would return the car in Rome anyhow. I don't know about this business of returning the car in Orvieto. If one had to go from Lake Tahoe/Reno to San Francisco, that person wouldn't return the car in Sacramento and take the train from Sac to SF (about the same distance as Orvieto to Rome). It is a mystery to me why Americans subject themselves to this nonsense when they travel to Europe, when they would never do it at home. All major rental companies have at least a dozen drop off locations to choose from in and around Rome.

I think your itinerary is reasonable but perhaps I would cut a day off near Florence and spend a day in Orvieto, one of my favorite spots.

I would also pick the car up in La Spezia. Don't be afraid of driving in Italy - it's not that bad especially outside the cities. Hopefully you know how to drive a stick as you may reserve an automatic but in Italia you get what they have

The only weird thing with your itinerary is that you potentially train through Florence to get to 5 Terre. Then backtrack. But that is no biggy and maybe you are going a different way.

Stop by Panzano and look up Dario (Google Dario Cecchini)

Roberto is right on, rent in La Spezia and drop in Rome.

Your itinerary looks great for a first timer in Italy. Good work.

I would stop and visit Orvieto but drop car off nearer to Rome or at FCO airport, an easy access from the autostrada. Then book the company we use for transfer to your hotel. Reliable and about the same price as a taxi www.romelimousines.com.
We use some trains but find a car so very much easier. We parked our car for three nights in the Cinque Terre. I hate sxhlepping bags on and off trains even small ones. We pack light, 22" rollaboards.. If you use trains, do not take more than that size luggage.
Book your cars through www.autoeurope.com, a broker in Portland, ME that stands behind you. We have used rhem for many years. Call them if you have questions.

Thanks to all who posted. I'm taking your suggestions on renting the car in La Spezia, and returning it outside Rome. Your comments were very helpful!