A stop in Florence is perfectly feasible. There's a great baggage checkroom in the train station (toward the left as you exit the train platform). The center of historical Florence is relatively small, so you'll be able to wander past the Duomo--do visit the inside of the Baptistery--and wander to the famous Ponte Vecchio. If you want to see David, make an effort to reserve a timed tickets so you won't waste your brief visit standing in line.

Venice is like no pleace else but 2 days there will get you all you want. From there take the train to Rome and spend at least 5 days. Rome is an amazing city full of life , amazing sights and the best food. You won't be disappointed.