I'd fly into Venice out of Rome if possible - unless your flight out of Venice is not early (try to avoid taking a very early flight out of Venice - can be expensive to get there early if you can't use the airport bus!).
Otherwise, it's a matter of optimizing time, cost, and convenience. Go on Google Flights and do some searching. Note, you want "open jaw" or "multi-city' and NOT two one-way tickets! You want an open jaw (into one city, out of another) on a SINGLE ticket.
If it's super cheap to fly into/out of Rome vs. the open jaw with Venice, you could take the train to Venice (or Florence) immediately upon landing and start there then train back to Rome at the end and do all of your days in Rome together. But that costs you half a day extra of train travel, and you have only nine days, so that would not be ideal.
I assume 9 days means 8 nights - and one night in the air(?) so that might really mean only 7 nights in Italy. In that case, that's going to be a very quick trip.