How far in advance to buy train and bus tickets for family?

If you want to get the lowest fares with advance purchase, train specific tickets, the price goes up as the lower tiers of tickets sell out, so purchase them online as soon as you can commit.

I like to use www.rome2rio.com to see what the options are for each leg of a trip. In the left column, you can click on the link, I.e. Trenitalia for most Italian trains, etc.

The cheapest fares for the train tickets are usually available on-line about 3 months before the date. You can save a lot of money purchasing them ahead of time, but they are non refundable and similar to a plane ticket in that you have a specific train time and specific seats reserved. But, I usually know that I’m going to travel mid-morning on a trip, so I purchase mine ahead and have saved a lot. Those cheap tickets go quickly, so purchase them as soon as available, or they’re gone.

If you buy tickets at the station, you MUST validate the tickets before you get on the train. (Big fines on the spot!). There’s a small machine at the stations to validate your tickets. If you bought them on-line ahead of time, they don’t need to be validated.

Your drivers’ licenses are USA documents. Valid ID in Europe are your passports.

Also, I wouldn’t plan any bus travel or obscure train travel on Sundays when it’s more sporadic and less reliable. We’ve been stuck at a train station on a Sunday, hoping a subsequent train would show up.

Some of those trips look like regional trains. The prices of those do not increase as you approach the travel date, and they cannot sell out, because there are no assigned seats. You may run into some overcrowded trains over the Christmas holidays. If they are unreserved trains, you stand (or sit on your suitcase) until someone gets off and you can snag a seat. You should not expect always to find five seats right together on an unreserved train unless you board at the starting point. Most of the time you probably won't have an issue.

You can check the type of train (but not the fares) very easily on the user-friendly Deutsche Bahn website. An "R" means a regional train with fixed fares. "FA", "FB" or "FR" is a fast Freccia train with mandatory reservations and escalating fares.

No one else has commented, so I will: That looks like an awful lot of places and an awful lot of traveling around for three weeks. It will be worse if you only have 19 nights in Italy. Every time you change hotels you lose at least half a day, and some of your location shifts will take longer than that. A day with a hotel change is just not very productive by the time you get settled into your new place. Also remember how early it gets dark in December. You're not going to have that many sightseeing hours per day.

I think I'd want to spend at least 5 nights in Rome, 3 in Florence (plus extra for day trips) and I know I'd want 3 in Venice. Then you have all your other locations.

Assisi is very far from Rome and Florence when you're considering a day-trip. Although it's not terribly far from the caves near Iesi, public transportation looks challenging and will not be fast. I believe the visit to the caves will be quicker than what you'll want to see in Assisi, so I'd prefer to base in Assisi and day-trip to the caves. (Note: I've never been to the caves.)

I really, really like Puglia, but getting to Alberobello is a major time commitment, and I'd want to see some other destinations in the area if I were going to spend so many hours on the train.

I'm guessing La Spezia is intended to allow a visit to the Cinque Terre. I haven't been there in the winter. I'm afraid it may be disappointing.

acraven makes a great point. You have eight stops, not counting day trips to Volterra and Assisi. Yikes! It might be a good idea to sit down and stare at your itinerary and a calendar simultaneously. Are your hotels already booked?