Transportation help from Switerland to Italy

Car is of no help for this itinerary, plus if you rent in one country and drop off in another, there is a large fee.
In Italy, point to point train tickets are best. In Switzerland, you will probably at least want the half-fare pass. It really depends on how long you will be there and how much moving around you do, what mountain excursions you plan on.
Are you flying into Zurich and out of Rome? You will probably come through Milan via train en route south.

How long will you be in Switzerland and specifically, at each place, Zürich and Grindelwald? You may benefit from a Berner Oberland Regional Pass and a Half Fare Card.

Train is absolutely the solution but there will be a longish transfer day to either Florence or Rome.

If you want to rent a car, wait until you cross the border into Italy. Or you do what we did, rent car in Italy, drive into Switzerland and tour where you want to go. Then cross border back into Italy, see more of Italy, return car back in Italy. We rented the car in Milan, drove to Switzerland, spent two weeks than entered Italy again, went toLake Como, then returned car at MXP for dlight to USA.

Thank you for all the great responses. We plan on being in Switzerland for one week (A few days in Zurich and a few days in Grindelwald area) and Italy for one week. Yes, the plan is to fly into Zurich and fly out of Rome.

Best to do is get the Half Fare Card. You can get that on arrival in ZRH. Or order it in advance on
https://www.sbb.ch/en/leisure-holidays/inspiration/international-guests/swiss-halffare-card.html

This gives you 50% off on all transportation in Switzerland. Also on mountain railways and cable cars. If you really plan on taking a lot of cable cars etc... you can combine that with the Berner Oberland Pass. Getting that pass, and then using it to the max is a good strategy. Nobody says you can't go up on the Männlichen a second or third time, just to get a beer. (I do that quite often...)

I would skip Zurich. Just go directly to Grindelwald (or wherever you plan on staying in the area) from the airport.

Then book Grindelwald - Florence on www.sbb.ch. You do not need to have the HFC already in your possession in order to be able to apply the reduction to that ticket. Just select Half Fare Travel Card under reductions. Booking this ticket in advance will save you money, but in theory you would be able to just buy it at the station in Grindelwald as well.

Florence - Rome book on www.trenitalia.com

Florence - Rome book on www.trenitalia.com

or on www.italotreno.it/en , the private competing company that runs only high speed trains. And that is often cheaper than trenitalia.

Same for the Milan-Florence leg. Always Compare Trenitalia's and Italotreno's fares before buying.

We spent 5 nights in Wengen, after coming from Italy, this summer. We had a rental van because we were spending a total of 3 weeks driving around Europe with 6 people. The van was parked in the Lauterbrunnen garage the entire time. We traveled by train/boat/gondola all over using the Half Fare Card plus the Berner Oberland pass. I kept track of our journeys. Paying full price, we each would have spent over 800 CHF, so the pass was worth it. Use the HFC to purchase discounted tickets from Zurich to Grindelwald. I agree with spending the majority of your time in the BO area.

I do not prefer a car to a train in Italy, especially if you are going to big cities like Florence and Rome where having a car is a real nightmare. The only way a car makes sense is if you are going to remote areas with lots of people (as we did). Then it is worth it for the time savings and possibly cost savings.

For the Milan - Florence leg I would not advise going with Italo, as the OP is coming from Switzerland, and you do not want a break of operators, in case the inbound train to Milan is delayed...

I can't thank you all enough for all the information you gave me!!!! This will help so very much.

I would definitely not recommend renting a car as the trip will take longer than by train. The high speed trains in Italy travel at 300 km/h so no cars can match that. Also, there are some potentially expensive caveats to be aware of when driving in Italy.

The others have already provided lots of good tips on travel passes. I would also suggest skipping Zürich. If you'd like to spend a few days prior to going to Grindelwald, you might consider Lucerne, as that's an easy trip from Zürich airport.

You can check all train routes using the Bahn.de website, although you won't be able to buy tickets from that website. I checked briefly and one of the quickest trips from Grindelwald to Firenze SMN is a departure at 10:48, arriving 17:04 (time 6H:16M, 3 transfers). Of course schedules can change so you'll need to verify closer to your trip.

There are also a few potentially expensive caveats when using trains in Italy. The express trains such as the Eurocity and Freccia have compulsory seat reservations which are specific to train, date and departure time. You can only board the specific departure listed on the ticket as if you board the wrong train by mistake, you may face hefty fines. If you need further information on using trains or public transit in Italy, post another note.