Someone above suggested to book a hotel in Rome the first night.
I would not do that. That would be a waste of time and money. A hotel in Rome will cost you more than 4 discounted tickets at the "Supereconomy" fare (or as much as two full fare "base" tickets). In addition changing hotels is time consuming. You are already planning to stay in Rome at the end of your trip.
Your choice to head to Venice upon landing is, IMO, the right choice. You can rest during the 3h45min train journey.
Regarding pre purchasing discounted tickets, you received great advice above, especially from Zoe. Savings are big, but there are risks involved since planes don't always land on time.
The chance of seats being sold out to Venice in February in any class (including 2nd/standard class) is less than zero percent. It never never happens. To prove this point, check the Trenitalia website tonight when it's morning in Italy. You will see that no trains will be sold out in low season. However only full "base" fare will be available on a same day purchase.
If you were traveling in high tourist season, then some trains could have their second class (standard class) sold out in the early morning trains. In that case you would need to upgrade to the more expensive first (business) class (which never sells out, not even in high season) or wait for a train departing in the late morning (which rarely, if ever, sell out their standard class seats).