OP, In Venice, you would also have a 5 or 6-minute walk from Santa Lucia train station to Piazzale Roma, over the badly misconceived bridge with the variable-pitched stairs (Ponte della Constituzione) where a misstep is practically unavoidable (I had a few) and you have to lift and carry your luggage.
If you take the train, don't go all the way into Venice (and, of course, don't take the water taxi). As mentioned above, get off at Mestre. You will be a little closer to the airport than from Venice proper, and also earlier by 12 minutes. The ATVO bus is the airport shuttle, just turn right as you exit the train station. Unlike in Venice, the bus is directly at the train station. It runs to a similar schedule.
According to the official time table, the bus from Mestre should take less than from Venice (17 minutes vs 20), but when we took the 7am bus on a Friday, it took almost 30 minutes, making frequent stops for commuters and schoolchildren (yes, it was the ATVO Airport Express, not the regular ACTV local bus). There should be no such problem on a Sunday.
The taxi rank is right at the train station exit, it may be your best bet. It should cost between €40-50.
ETA: As mentioned above, you should take the earlier Italo train (biglietti.italotreno.it). The are no more seats left for tomorrow, seats are available for the other Sundays. You should book in advance (the cheapest tickets are €24.90 pp).
Let us know how it went.
Last edited by FlyerTLV; Nov 3, 2018 at 9:31 am