Venice to Munich

The most affordable way would probably be to walk. Or have someone else pay for your transportation.

Bus is probably the cheapest reasonable way to go, but if you buy a train ticket far in advance, the difference might be negligible. Flying on a LCC (again, ticket bought well in advance, and not paying for any "extras" might be almost as cheap. Train or cheap airline would probably be my two "best" options. Train = more comfort, flight = faster.

The answer to questions like this usually depends on your priorities.

Here is a menu of choices

https://www.rome2rio.com/map/Venice/Munich

Bus seems to be the cheapest

Treat yourself with one of the better train rides in Europe by taking the route via Verona and Bolzano, going right through the Dolomites mountain range.
Advance-bought tickets can be as cheap as EUR 60.

Added:
Trains come without hidden costs. Luggage is unlimited and free. No booking fee. No penalties if you forgot to print out your boarding ticket.

No doubt in my mind - take the direct 7 hour train from Munich to Venice S. Lucia.

Thanks, everyone for your input. Do we need to buy train tickets before we leave US? They are pretty expensive online compared to what we have paid in the past. The last website I searched was Trainline.

What date? I am paging through the Deutsche Bahn site for direct day trains in late July and they are all either, 49.90, 59.90, and 69.90 EUR per person for Sparpreis Europa tickets. That is not exactly exorbitant.