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Someone has already given you the Italian train website. Stan's advise to take an early train to Pisa is good - you have a couple of options depending on how you value speed vs cost. There's a regional train at 6:09 am from Roma Termini that will get you to Pisa at 10:15 am (4 hr 6 min) at a cost of 17.15 euro. The other choice is the ICplus train at 7:35 am that gets you to Pisa at 10:57 am (3 hr 22 min) for 27.50 euro. If you buy the ticket at least one day in advance, you might be able to get the discounted Amica fare for 22.40 euro.
Pisa to Venice requires a change in Florence and takes 4 hr 12 min to 4 hr 55 min depending on the connection. The cost is 29.10 to 37.90 euro depending on whether you take an intercity or Eurostar train between Florence and Venice. It's a regional train from Pisa. You can save a little money if you buy the tickets as two separate trips. The regional train does not have an Amica fare, but the higher speed trains from Florence do if the tickets are bought in advance.
I would also take the train from Venice to Rome. A Eurostar will take about 4 and a half hours, and cost 56.10 euro at the standard fare or 44.90 at the Amica fare. However, there's a better option. There's a night train at 11:30 pm that arrives in Rome at 6:56 the next morning. You can book a seat for 36.50 euro standard or 26.80 at the Amica rate. It will be easier to sleep if you get a berth in a 4 bed compartment for 56.50 euro or 45.20 euro Amica. There are a couple of advantages to this - you get more sightseeing time and travel while you sleep and you don't have to pay for a hotel or hostel for the night.
I would not bother with a flight - the budget flights between Venice and Rome leave from the Treviso airport. While there are flights as low as 30.16 euro on some days on other days the cost is 80 euro. You will also have to pay for transport to the Treviso airport and from Ciampino airport into Rome. While the flight time is 1 hr 5 min, you need to factor in an hour from Venice to Treviso and arrive at least an hour before your flight. Then there's the time to pick up any baggage at Ciampino and get into Rome. The train is much more convenient and most likely cheaper.
http://www.bookryanair.com/SkySales/FRSearch.aspx?culture=EN-GB&pos=SBFORM.
A flight from Marco Polo airport will cost over 90 euro. The cheapest option would be Air One or Alitalia to Fiumicino airport.