Return trip to Italy in 2025, which month?

Stay away from the weeks before and after Easter, April 20, 2025. Those Easter weeks are crowded even without the Jubilee. We were in Italy May, 2023 and had record amounts of rain, over two weeks, which wasn't ideal. In Venice alone, we had 48 hours of nonstop rain. Predicting climate these days has become impossible.
I'd suggest longer in Venice, and perhaps Lake Como? You could then fly open jaw, into Milan and out of Rome, maybe.
But I digress, that wasn't your question.
Shoulder seasons are disappearing, post covid, and avoiding crowds is difficult. In Venice, we stay in the Cannaregio area, on the quiet back canals, where one can take sunset pictures without a soul spoiling the frame. So when the San Marco area is packed, "our" area of Venice is charming and peaceful. And- there are many great day trip from Venice, such as Padua.
So happy that you had a wonderful adventure, and want to return. Have a great time planning. Safe travels!

My favorite month to be in Rome is January (after the 6th which marks the end of the Christmas holidays). The city seems to let out its breath and relax. If it doesn't rain, there can be incredibly bright blue skies and sunshine, and a light jacket is all you need for the moderate temps. It's the least crowded time. Unfortunately the period you are proposing is peak season. January-February-March would be much better. I agree Orvieto is a perfect day trip.

”I have an addiction, the best kind there is…”. And, there’s no known cure - LOL! I was in Italy again this year and already have my plane tickets for next year.

I went for the month in May this year, and the weather was very good, although I was mostly in Puglia & Sicily - a few days in Rome.

I’m taking the Jubilee crowd serious, so although I am flying into/out of Rome, I am only spending my arrival day there and last night at a hotel at the airport. I would go back to Spello, but not this time since it’s near Assisi. As you’re researching & making plans over the winter, consider staying at some “secondary” locations, too. The crowds aren’t at those locations, so they are very pleasant. I’ve stayed at 39 cities in Italy and have rarely been to one I would not return if given the chance.

In mid-March 2023, my family spent a wonderful week in Rome and Florence, enjoying perfect weather and manageable crowds. Next year, we're planning a week in Venice and Milan around the same time, hoping Mother Nature will be just as generous!

So happy of hear that you had a great trip!!!! I've a lot of specific questions about how some of it went for you, such as how was your birthday? How was the Keymaster's tour at the Vatican? Were you able to access the Uffizi library? Etc. etc!!!! Ramble away, please!

Sooo, if I was to roll the dice on the next trip, I might think about end of March into beginning of April: in and out well before Easter. Temperatures are historically pretty moderate, and although April is wetter than March, there's really no way to accurately predict what may be thrown at you. I wouldn't do May. We've done that one and while most days were dry, crowds were pretty dense although we were able to work around the worst in Rome by skipping some biggies we'd already done. Florence in May was very busy but, well, the crowds may well have been invisible for the stars in my eyes! Like you, I fell end-over-teakettle for Florence. Just like Rome you'll also have the ability to skip some of the most-visited attractions, if desired, and concentrate on some of the less overrun treasures.

March is, in my experience, a very nice month in Italy, the later the better. April is good, too, a little more crowded but you can work around Easter with smart planning.

September is still very warm. Not sure about October being a rainy month. We have been somewhere in Italy nearly every October since 2010 and it was usually good.

This year all I can say about the weather is that it was unstable. We were in Switzerland, northern Italy and Rome and it seemed the forecast for the next day or two was seldom right. The rainy day one day did not materialize but the expected sunny day the next did not either. Only in Rome did we have a string of nice days and we just left there this morning. Ironically, they-who-do-the-weather even got it wrong on a hourly basis one night resulting in our being soaked to the skin on a walk home from dinner when the forecast said “no rain in sight for several hours.”

My point overall is this: you cannot game the weather. We have had hot and dry years in Italy where the country was in dire need of rain, and we have had ice and snow in early September in the Dolomites more than once, including this year. The following days were back to seasonally temperate so an anomaly, I guess. Travelers have always sought and hoped for good weather. Before climate change became so profound, we may have gotten what we wanted more often. The reality now is wild swings and seasonal unknowns.

Do not wait. 2025 begins on the 1st of January. ROME in January is wonderful and very satisfying. Should it rain there are enough indoor attractions to last at least seven years. I had only sunshine. The Jubilee year that concerns so many will probably be at its least noticeable.

Consider walled LUCCA, the cozy Tuscan town that is an attraction in itself.

Not sure if this would work for you-
Google Flights just alerted me to decent business class prices between LAX and Milan for May, 2025. Found business class seats for around $2600 RT on British Airways. Sometimes there are other cheap routes when this happens. Maybe this determines when you go. Good luck!

which month for warm (not hot)/drier weather and least amount of people

I think safe to say that warmer/drier is directly proportional to number of people.

But, we were there the first 2 weeks of November 2024 and found large crowds in Rome even then. The weather was generally warm - there was a fair amount of rain falling overnight - only a few showers encountered during the day in Rome - although heavy rain one day in the CT.

So if you are crowd-averse, the "winter" months may make more sense, as cited above. Here in Los Angeles, I have morning coffee outside on sunny days 12 months per year - climate in Italy not dissimilar. Plus, airfare will be lower, which I believe was a major concern for you.

You might consider Siena instead of Florence for part of your time there, and an overnight stay [or two] in Orvieto on the trip to Rome from Florence may be more rewarding for you.

I was on the VFR tour at the end of October to beginning of November 2022. The weather was warmer than usual and we had no rain except the morning we went to the Vatican. It was nearly perfect.
Rome had crowds but not overwhelming numbers. I fell in love with Venice despite not expecting to like it at all. The only drawback to that time of year was that it got dark fairly early. I would return to Italy anytime except summer when it’s too hot and crowded for my liking.