Driving from Fiumincino Airport to Concha die Marini (Amalfi Coast)

Also, any safety concerns

If you are planning on renting the car after a flight from the U.S., please reconsider. You will be tired, sleepy, probably jet lagged, and on unfamilar ground. Perhaps you are not bothered by those things, but for many others it is an accident waiting to happen. Even small fender bender at the start of a trip will put a damper on the entire trip. Perhaps an overnight in Rome and pick up the car the next day? Don't mean to rain on your parade, just offering food for thought.

Anywhere on AC is the last place I would want or need a car

Yes Italian freeways come with rest stops that are fully equipped with cafeteria style restaurant, mini market, restrooms, shower facilities, baby changing station, fuel station. Just keep an eye for signs saying AREA DI SERVIZIO. There is one every 20-30 km and you don’t need to exit the freeway they are like rest stops in the US Interstate system (which however have only restrooms as Federal,law prohibits the commercialization of rest stops on US Interstate highways.

As Christine mentioned, you may be jet lagged if traveling after an intercontinental flight. The drive is in part a very boring freeway driving (very sleep inducing) followed by the last 30km of the crookedest road you have probably ever driven with hairpin curves ona very narrow road with walls and ravines on either side. Therefore be very alert. The total trip is about 4 hour long, plus pit stops. If you want to minimize driving time you could also take a fast train to Salerno then rent the car in Salerno. In that case no freeway driving necessary, but you still get the scenic exciting drive with the curves and the ravines.

Freeway driving rules:
-The left lane is only passing lane. No cruising allowed. If you linger on the left lane one second too long after passing a vehicle Italian cars will be aggressively tail gate you at 80 mph at no more than 5 inches from your rear bumper while flashing their lights and honking their horn until you move back to the right lane. That is a very unnerving experience to American drivers, but that is the way it is.
-When you merge onto the freeway from the ramp you must be careful because the merge is sudden and there is a yield sign before merging in. If you cannot merge because of upcoming vehicles you must stop on the merging ramp. Don’t expect Italian drivers to move the the left lane to let you in.
-Be careful of truck drivers. They will change lanes and cut you off without warning. They are bigger than your car and they don’t care if they squeeze you against the median guardrail at 80mph. That is true regardless of the nationality of the truck drivers (most of whom are Eastern European immigrants)
-You cannot pass another vehicle from the right, you must pass them on the left using the left lanes. Occasionally some might pass on the right, because Neapolitans don’t believe in rules, but it is prohibited and dangerous.
-On toll freeways speed is checked by camera using the speed tutor system. They basically calculate your average speed in 10 km segments. Your average speed cannot exceed the speed for that segment (usually 130km/h).
-Outside of toll freeways speed is checked by automatic cameras that take your photo if you exceed the speed more than 5 km/h above the limit.
To pay toll see below
https://mominitaly.com/how-to-pay-tolls-in-italy-autostrada/
https://www.autostrade.it/en/il-pedaggio/pagamento-al-casello

Agree with not wanting to do any jet lagged driving.

Best choice would be to take a quick flight from Fiumicino to Naples Capodochino airport, and have a driver waiting for you there, to take you directly to Concha die Marini. Or try renting a car right there in Naples, but I don't know if I'd want to do that jetlagged either!

If renting a car for other travel in Italy, you can always do that after you get your sea legs. And driving on the A.C., I would say all year long, is either not for the faint of heart or total gridlock--pick your poison.

Roberto, thank you so much for the info
We go to Lake Como every year and drive from Malpensemto Bellagio, so we are very used to narrow windy roads after a long trip
Roberto, thanks again

Good. Then make sure you get a couple of double espresso at Fiumicino before driving down to Naples.
The road is narrower than to one to Bellagio (basically one lane wide but traffic goes both directions) and there are lots of hairpin curves. So be careful.
Having said that, based on your accommodations (5km in the interior and with parking), having a rental car is the proper choice.