Trip to Italy mid-late Nov

The only reason (but it is a good one) to purchase train tickets in advance on-line is to take advantage of any discount tickets that might be available. However, the discount ticket come with restrictions - no change, no refund and sometimes one change allowed - all depending on the ticket class. You don't have to worry about tickets being sold out since that rarely happens. Trains are frequently and large.

You can hit both in one day easy. You are only allowed two hours in Borghese anyway and the Vatican is easy to see in couple of hours or so. The museum could take longer.

If you haven't purchased your airline tickets, you should opt for an open jaw ticket - into Venice and home from Rome. Cheaper and more convenient than your round trip from Rome. (It is easier to go into Venice and home from Rome rather than the reverse.)

I'm with Frank but I'm guessing you've already purchased your airfare. Assuming you have, you can at least improve the situation by pulling out a city. If you've never been to Italy before, you would be fine limiting yourself to Rome, Venice and Florence. In fact, with your short trip and your committed arrival/departure from Rome, you might have a better time if you just do Rome and Florence and that's hard for me to even suggest because I love Venice more than anywhere else I've ever been.

If you want to do all three cities it might be easiest to land in Rome and then head straight up to your most distant city. Are you landing on the 17th in the morning? Then head right to Venice. Stay in Venice 3 nights (17, 18, 19), train to Florence for nights (20, 21) then train to Rome (22, 23, 24). It's tight this way and you'll miss a lot of Florence, but okay for a first trip.

Be aware that just about everyone who has been to the Vatican recently reports that the Sistine Chapel is an utter mob scene. I'm not clear on what other areas are massively overcrowded. If seeing the Vatican is important to you, explore the possibility of visiting outside the public viewing hours by taking one of the tours that get early access. This comes at a higher cost, but it really sounds like it is pretty much mandatory to have a decent experience.

In some manner or other you need to pre-book the Vatican Museums (by tour or otherwise), and the Borghese requires pre-booking.

I think you would be "safe" to purchase tickets as needed as the trains don't fill that often. The only real reasons to purchase in advance are to save (a little bit of) money and keep a large group together in one carriage.

My advise would be to stick to just Rome or just Rome and Florence (Tuscany) for such a short trip. But, if you really (really!) want to see Venice this trip, and you've already purchased airfare, head straight to Venice and work your way back to Rome. That will give you maximum flexibility in your travel plans... If you arrive FCO in the morning, you can be in Venice by suppertime pretty easy (the 1059 direct train from the airport gets you into Venice at 1530).

Other things to take into consideration. Venice in November will have about 9 /13 hours of day light while Rome will have 20 or so minutes more (another reason to start the trip in the north and work south). Venice's high temps are mid to upper 40s to low to mid 50s while Rome averages 10 to 15 degrees warmer. And, you are out in the weather quite a bit more in Venice whereas Rome (or Florence) has a lot more opportunities to get inside on inclement days.

Just a quick reminder...
If you leave the U.S. onthe 17th, you arrive in Rome on the 18th.
You might check out flights Rome-Venice on your arrival day. Alitalia flies there as reasonable as the train, and since you're already at the airport it might make sense.
Just be sure to allow 2 1/2-3 hours between arrival and departure.

Helpful information, thanks!
Does anyone know if the Borghese Gallery is closed after the 13th of Nov? Have emailed the gallery x2 but no response.