Venice to Rome or Rome to Venice?

It's going to get colder over time so it would be best to go north to south.

I find Venice a little easier city to get over jet lag and Rome a little easier to get an international flight from, but neither a good enough reason if you want to start in Rome and end in Venice. Buon viaggio!

The other reason to start in Venice is that if you end there, often you have to take a flight very early in the morning to connect in another city European city to get back to North America. It is a pain to get to Venice airport at 5 am to get those flights. And if you have to take a water taxi, its expensive. Rome has lots of direct flights to North America beginning about 11:00 am, so you can connect to your home town airport in North America.

Simply logistics. It is far easier to depart from Rome than Venice. Much better airline options. And easier access to the Rome airport.

Following up on Sam's point, for part of the year there are flights from Venice nonstop back to the US, that leave later. But these flights don't operate in December. A water taxi to the Venice airport is about €120. Sometimes you can use a night vaporetto to the bus station, then an early bus to the airport, but this means a VERY early wake-up call on your last morning. And sometimes you can get a later flight that will still connect that day to your home city, particularly if you live in a major East Coast or Midwestern hub like New York or Chicago. Or, you could fly from Venice to another city in Europe, spend a day there, then come home (say, a day in London or Paris, which have lots of options back to the US at various hours).

From Rome, there are year-round flights nonstop to the US. But even if you have to connect and have an early departure from Rome, a land taxi is €48 (fixed rate) and takes about 35 minutes.

Short version: before going any further with your planning, investigate flight options. If you are going to need early flights, investigate how you will handle the last night (airport hotel? early taxi?). Then, decide on the order of your trip.

Edit: Cross posting with Frank.

Thanks for the replies, we will check the flights carefully!

Go north to south for all reasons mentioned

Personally, I think the RS tours intentionally travel from Venice to Rome to allow travelers to work up to the immense scale and intensity of Rome. In 1995 I went to Italy for a 4 week study-abroad program. It was my first trip to Europe. We traveled southward, visiting Venice, Florence and Rome. I think it was easier for me to absorb everything starting in Venice, which was experienced on an intimate scale, eventually working our way up to Rome, with St. Peter's, the Vatican and the Colosseum on such a large scale. I think I would have been completely overwhelmed had we started in Rome.
I'm planning a return trip to Italy for sometime next year, taking my spouse to Italy for the first time, and I plan to start north In Milan or Venice, visit Florence and end in Rome. We're considering the RS 14 day Europe trip, or the 10 day Venice, Florence, Rome trip so we have more time in those cities. A big reason we're considering those RS tours is because of the order they plan to visit those cities.
Two years ago I planned a trip myself with my spouse and father-in-law to Austria, Switzerland and Germany and I underestimated how overwhelming it can be for some folks when traveling internationally. The train travel and multiple city itinerary was at an unrealistic pace for both of them and nearly derailed the trip more than once. Since then, we've taken 3 group tours (2 with RS) with much more success.
Now, when I'm planning our trips, I really study the itineraries of the RS tours and try to follow the suggestions in the RS guidebooks because I think there's a lot of wisdom to draw upon from taking thousands of travelers through Europe. As they say, your mileage may vary, and you should consider your travel preferences and factor in what you (and any other potential travelers) would prefer.

I think four cities is at least one too many for a trip of this length, especially in December when the days will be very short. Your arrival day will probably find you sleep-deprived and jetlagged, so the first (partial) day in your arrival city won't be very productive. If you have nine nights in Italy, I count that as only eight days. The more cities you visit, the less sightsering time you'll have because of the time spent dealing with trains and hotel changes. If you go to four citues, you'll have only five full days when you're not moving to a new city.

Definitely Venice to Rome for all the reasons mentioned. I would do 3-2-4 (Venice, Florence, Rome) on your stays arriving in Rome around 5 p.m. with three full days to enjoy. Forget Sienna on this trip, as much as it is a great city to visit, covering so much ground with relatively little time, you must cut somewhere.

Because flights to North America leave in the morning, and getting to VCE airport early in the morning from the city center, in the middle of the lagoon, takes a long time. There are also no direct flights from North America in winter, therefore you must connect at some hub in Europe. Rome airport is only 30 min from the city center.

9 days is not enough for all of those places. At most you can see Venice, Florence, and Rome, and even for that your vacation is too short.