Thanks for the additional info.
12 nights is not a super long trip so I would limit to 3 or maybe 4 locations.
Each location change eats up at least a half a day- don’t spend your time packing/checking in and out, traveling to and from /getting oriented and not just being there.
The only area that would probably need a car would be Tuscan countryside and you can see some of that on a guided bus tour or driver trip from Florence (we can make recommendations).
Train travel is easy and relatively inexpensive. Driving/car rental adds a whole other level of stress that you might not want (we have driven in Italy several times but for a first trip I’d say skip it)
The classic Venice- Florence-Rome trip is often referred to as the Holy Trinity. A lot of first timers do it because it covers the highlights and some important places- includes history, scenery, art, wine, food.
If you can change your flights (or haven’t booked yet) fly IN to Venice- much easier than flying out of Venice. Venice is the perfect place to get over jet lag - there is nowhere else like it.
A 3 night stay equals 2.5 days in that location.
Venice 3 nights- first day is arrival/jet lag day
Train to Florence- about 2 hrs
Florence deserves 2 nights minimum-more if you are really into art
add 1 night for every day trip you want to take (Lucca/Pisa, Siena or Tuscan countryside) so I would give it at least 3 nights
Train to Orvieto- about 2 hours
Orvieto- 2 nights- in Umbria but a beautiful hill town with amazing Duomo, classic white wine, great views and fun underground activities. It is right on the train line to Rome. This would give you a small town break between the 3 big cities.
Train to Rome- about 1.5-2 hours
Rome 4 nights or as much time as you can give it-you will never run out of things to see/do.
Fly home
On your way home- start planning your second trip which could include Amalfi Coast and other areas.
I just think the AC is such a time consuming hassle to get to and so very crowded that it’s not necessary on a first trip.