I would definitely stay over night on the island of Venice. Given that you are only there for a short time I would try and spend as much time as possible in Venice. I am not aware of a train that goes from Venice directly to the airport? The train station on the mainland is Mestre, and it is still a bus or taxi ride from the airport. From Venice, the island, you can take the Alilaguna water bus from various stations in Venice to the airport. Or, you can take the Vaporetto to Piazzale Roma and then take a bus or taxi to the airport. The train is not an option for getting to Marco Polo Airport.