Marco Polo airport to Padova

It depends. What is best for you?

Best for me, if I could afford it - unlikely -, I would hire a water taxi at the airport, and stand up or sit at the stern all the way winding back and forth across the Lagoon, and then around the end of the "fish" and up the Grand Canal to the train station at which I'd get a train for the short ride to Padova.

Otherwise, if you have to skip the beautiful and unique Venice, you can get the bus from the airport to Padova. That will be cheaper and faster but less romantic and far less exciting.

Yes, there are frequent buses from the airport to Padua. You can buy tickets at the window in the main hall. The bus route does take you over the causeway to Piazzale Roma to pick up passengers in Venice before proceeding to Padua. Luggage is stored in compartment under the bus. Validate your ticket on the bus.