First answer - it is going to be cheaper to get Euros at an ATM in the Rome airport. Cash in major
cities is not really needed these days, although it is nice to have some for whatever eventuality
might pop up. But use your bank ATM card, not a currency exchange. The straight exchange rate
is better and the fees are much smaller.
As for getting to Venice, you really have two options; train or flight. Buying an additional plane ticket
is risky, especially if you are checking bags. You would have to claim bags, recheck on the second
airline, and reclear security. If you miss the second flight because your first one was late, you're at
the mercy of the second airline to accommodate you. So it is not necessarily quick.
The flight itself is an hour, and the total transit time will depend on your baggage situation, what
the flight sched to Venice is, and how much risk you want to take on the potential of delays.
The train ticket will most likely be less than the plane ticket, but you have to take the airport train
into Roma Termini and then a 4 hour train ride from there. There are obviously more trains on the
schedule than planes.