Planes, Trains and Automobiles - Help please

Transportation by train in Italy is quite easy - almost mindless! Check trenitalia.com for schedules. When you can take the Freccia line, I suggest you do. The trains are comfortable and, by US standards, inexpensive and on time. If you want to commit to a specific schedule you can save because they offer very good discounts for early booking, class of service (1st or 2nd class has minimum differences), and specific times. None of your trips are more than 2 hours - Verona to Venice may have a change in trains which is no big deal. Enjoy your trip!

As long as you are firm with your itinerary I would book all but the train from Verona to Venice (I think that is local- so no discounts).

Other trains- Venice to Florence, Florence to Rome - if you book in advance you can take advantage of discounted fares.
And definitely book the train from Austria to Verona and flight to Berlin.

There are 2 competing companies running high speed trains along the north-south backbone: Trenitalia and Italotreno, a private company.

The first step to save money is to compare prices.

If you purchase tickets at the counter on the departure day you will pay the full walk up fares. These full fares are always displayed in advance together with the discounted ones, this way you can easily calculate the price of last minute spontaneity.

The website www.thetrainline.eu is going to be your friend. It will show you both Trenitalia and Italo schedules available with the advanced purchase, non-refundable discounts. Also seems to be easier to understand the purchasing process for some people with better acceptance of US credit cards.

Your flight from Rome to Berlin will only go up in price - possibly quite sharply as the flights fill. Book as soon as you are sure of your plans; if you are sure of your plans now, book NOW!

To find all options in this route, use Skyscanner: https://www.skyscanner.com/. And be aware that Berlin has two airports (Tegel and Schoenefeld) and Rome has two airports (Ciampino and Fiumicino). All four can work fine, but do be sure you go to the right one in Rome so you don't miss your flight, and figure out how you're getting from your Berlin airport to your accommodations. From Tegel to most parts of Berlin that visitors stay in, a taxi is about €25-30, so that's a good option; there are also various buses.

Thank you everyone for the great input. We are working on logistics and will follow up so that we can let you know what we did and afterwards what worked and what didn't. The advice is so appreciated!

Both Freccia and Italo trains from Milan to Venice stop in Verona, so also consider buying those tickets in advance if you wish to go to Venice by high-speed rather than regional train.

Not enough time in Florence and Rome.