What size of rental car for four tall adults with luggage?

What is your exact planned itinerary and where exactly are your accommodations in each locality? Having a car while staying inside cities like Rome and Florence is not only unnecessary, but a bad idea. Maybe you might not need a car at all.

Once you return with your detailed plan, we can give you better advice. For now I can tell you that 4 adults will need at least an intermediate car, if not a so called "standard" (which is a step above intermediate and is larger), not so much because of the stature of the occupants, but because of your luggage requirements. However be aware that renting a car of that size costs as much as 3 economy cars, therefore if your party would be willing to split, you will save by renting 2 economy cars rather than 1 large one. One economy car will be more than enough for two people plus luggage, regardless of size of the occupants.
Below is an example of the Europcar fleet:
https://www.europcar.it/la-nostra-flotta
A few years ago I had 4 adults in a VW Passat station wagon. The trunk, probably larger than my Subaru Outback, was enough for 4 midsize suitcases plus smaller backpacks. Plenty of room for the occupants too. That car is a "standard" size. I could have rented 3 economy cars for the same price, but I was the only driver willing and qualified to drive in Italy(and I would not want to be the passenger in any cars where the other members of my party were drivers while in Italy).

However, please come back with your detailed plans, from the airport you land to the one you depart from.

Whatever size you think you need reserve a much larger size. And if you really want that luggage to be covered and protected in the trunk of the car then don't get a station wagon or hatchback sort of thing. The station wagons have covers that supposedly "hide" your luggage...but that only works if your luggage fits nice and neatly in the space allotted. Otherwise when you pull the canvas covering over your luggage it will be bumpy and not smooth and edges and corners and wheels will stick out and still be visible...rather defeats the purpose of having the covering in the first place. I really hate rental cars and highly recommend if there's any other way to travel (and there probably is) choose the non-rental car mode of transport and save yourself some really big potential headaches.

Rental cars are such boat anchors around our necks when traveling in Europe.

It is true that departures from Positano without a car service or a car can be annoying to your itinerary. As others noted, you might consider whether you really need this car. What hasn't come up yet in this thread includes:
Small parking spaces and ramps in civic and commercial garages in Europe.
Likely substitution of vehicle by the rental company on pickup day.
Are you trying to get an automatic transmission? BIG issue.
Are you going to sight-see with luggage in the car, or just drive to hotels and unload first?
Do you know what a city ZTL is?

I have had great comfort in Ford Focus diesel station wagons, but I'm only 5'7", and our luggage "fit".

Another option would be to take a one hour train ride to Orvieto and rent your car there. This way, you can see this beautiful hilltown, get on the autostrada and head to your next destination. Even with a large, mid-size car last year, our group of three slim gals barely fit. It wasn't us, it was our luggage. We each had two carry-on cases, plus backpacks and purses and it was a challenge to fit it all in. Our luggage was never out of sight. Additionally, it was hard to drive and park this size car on the narrow village roads. Have a great trip seeing the hills of Tuscany.

One other point to mention is that each driver listed on the rental form will require the compulsory International Driver's Permit, which is used in conjunction with your home D.L. I.D.P.'s are easily obtained at any AAA office for a small fee, and are valid for one year.

Also, as mentioned in other replies be sure to do some research on ZTL (limited traffic) areas, as hefty fines will result for each pass through one of these. Do not drive in Florence as the city is just about saturated with automated ZTL cameras.

We plan to pick the car up as we are leaving Rome and headed to explore the Amalfi Coast. Our hotel in Positano has its own parking lot as does our hotel in Tuscany. When we get to Florence we plan to turn the car in when we arrive so no parking there. We have considered taking the train to Naples and picking the car up then but there seem to be fewer choices of vehicles. We will have a few days when we will have our luggage in the car with us as we stop and explore while we are driving from one city and hotel to the next. That is where the dilemma comes in with which category of car to rent so that we can keep our belongings out of sight.

Whichever car you choose, plan to take a daybag with you while sightseeing and leave nothing of great value in your parked car.

If you plan to drive the coastal road, you will be very sorry to have a large vehicle. I always get the smallest vehicle I can. Last fall, my 2 cousins and I, who are all women under 5'3, had a Fiesta, and only our wheelies fit in the trunk, rest had to go in the car. You should seriously consider 2 vehicles or a van, but then take a taxi or tour bus rather than drive tthe Amalfi. I have driven it twice, and it takes skill even with the smallest vehicle, given how narrow the road, and oncoming tour busses.

That is a lot of luggage and will complicate your space requirements. We had mid-size for four adults with one rolling carry on. The four carryon bags fit perfectly in the truck - four across but that was it. No addition space except maybe for an umbrella and a couple of jackets.

Now that I have your detailed itinerary, I can say that I think your plan is good. I'do the exact same.

Now the issue is to decide whether to rent 2 economy cars or one large enough for 4 adults with quite a bit of luggage. Based on the luggage you intend to take, I think you need a 'standard' size car, which as I mentioned above, would be like a Station Wagon or large sedan.

Two economy cars would be cheaper than one large one, even once you consider the additional fuel and freeway tolls. Two economy cars would offer also more flexibility, in case some members of your party want to do something different. Once you drop your luggage, you can also take small trips around in one car only. Squeezing 4 big people in an economy car will be "fun", but for short day trips without luggage you can certainly manage. Economy cars are also easier to maneuver in small ancient streets that characterize many Italian towns. Having said that, however, it is also possible that no additional members of your party may be willing to drive. That I don't know. Just do your research, discuss it, then decide.

My suggestion now is to go to www.autoeurope.com or www.kemwel.com (two consolidators part of the same corporate group) and check prices and options for both two economy cars or a large standard. They work with the major rental companies, but generally offer better deals than directly.

Note that the above websites call the "standard" size "family size". That is what you need if you decide to go with the one car only option.

Regarding the possibility of manouvering a larger car in the Amalfi coast or in Tuscan towns. It is certainly true that an economy car will be easier to park in smaller spaces, however don't let yourself be terrorized by some of the posters. I often drive large cars there, and many of my high school friends in Italy have very large cars and SUVs. They survive and so will you. Just make sure the designated driver in your party is the most skilled behind the wheel.

Although Naples is not on the Amalfi Coast, you do mention the city as if you intend to visit it. It certainly is an important site for art and European history.

I mention this because if there's any place that's harder to drive and park in than an average European medieval town center, it would be Naples. It's almost hopeless to navigate a wide car through the narrow streets and bollards, with cars illegally parked half-on, half-off the street, and lawless parking in plazas and on zebra striped areas. (I didn't drive there, I'm reporting from looking out our hotel window, and from walking around on two successive days.) Count on scratches if you drive or park in Naples.

There seems to be no talking people out of driving the Amalfi Coast. Our driver (8-hour booking from our hotel in Sorrento) had to stop repeatedly on the two-lane, single road, so that busses could back up and make sharp turns, or to get around people who had stopped to look at the view. I don't think you gave the month of your trip, but in high season, this problem is acute. I didn't think the road was any "scarier" than hilly roads in Vermont or Utah - the issue, to me, was the savage traffic. We didn't have to worry about parking because our driver went somewhere else during our "free time" in Amalfi, Ravello, and Positano.

A couple of comments based on your last post:=

Our hotel in Positano has its own parking lot as does our hotel in Tuscany.

Just because your hotel in Positano has its own parking lot doesn't mean that the car you are driving will fit easily into the parking space. Many hotel spaces are very small, and they may well not be attached to the hotel but part of a common lot with assigned spaces, or they might. The problem is often getting the door open after slotting into the space, and possibly parking on a steep hill as Positano is on one (hence the views). It might be worth getting a bit more detail from the hotel.

If you are in a hill town in Tuscany, what I said about Positano may apply there too. If you are out in the countryside at an Agriturismo they may well have plenty of space.

When we get to Florence we plan to turn the car in when we arrive so no parking there.

Please understand that the huge fines for ZTLs are for driving in restricted areas, not for parking. You only need to be in a ZTL long enough for the automatic cameras at each entrance to photograph the car. And if you go in circles you get a new fine every time you pass the cameras.

I agree that the major problems with the Amalfi Coast driving is the traffic, and that the views are pretty cool so the driver is tempted to take his/her eyes off the road. Especially problematical when both directions of cars are driven by tourists at a particularly beautiful spot, and then there is nowhere to stop.

I love to drive there. It tests my skills and that's just how I like it. My wife - she in the passenger seat - hates it. (loves the views hates being in a car there)