Travel to/from Train Station:  I am not sure who designed the Venice Santa Lucia train station but they did not have travelers with heavy luggage in mind, although it is accessible to the historic district of Venice and near water transportation.   The options here are to take a vaporetto (in essence, a bus that travels on the canals) at 7.50 euro a trip.   The vaporetto is slow.  For instance, it can take about 40-50 minutes to get from the train station to St. Mark's Square.  It can be very, very crowded and not well-suited for taking bulky luggage on or off the vaporetto.   Also, at the train station, a wait of 15-20 minutes to buy a ticket is common on a crowded day.    Another option is to take a private water taxi at a minimum of 60 euros per ride, but they will get you closest to the hotel in the fastest amount of time.

On our Traveling Professor small group tours to Venice we always take a water taxi directly to the hotel.

Traveling to/from Airport:  Again, the water taxi is most direct and probably takes about 30 minutes.   But it will cost a minimum of 120 euros.   The AliLaguna shuttle service takes about 75 minutes and you need to travel on their schedule from their pickup/drop off points.  Cost is about 17 euros per person.

Travel Around the Historic Area:  As mentioned, the historic district is very walkable.   The vaporetto is not a bad option here.  As previously mentioned, it is 7.50 euro per trip but a 24-hour pass can be purchased for 20 euros (does not include transportation to/from airport).  A traghetto is a small gondola-like boat that transverses larger canals.  It's good for taking a "short cut" but not if carrying bulky items.  Thanks to Rick Steves popularizing the traghettos, it will now cost you 2 euro to use it, although locals still get it for 50 cents.