Train from Venice Italy to Munich Gemany

The station on Venice island is "Venezia Santa Lucia", often abbreviated to "Venezia SL". "Venezia Mestre" is on the mainland, and not the one you want.
The main station in Munich is "München Hauptbahnhof", abbreviated "München HB". The main station in any German or Austrian city is always called "HB".

You can look up times on the German Railways site: https://www.bahn.com/en/view/index.shtml
This will always find you the quickest route, you don't need to know which line is best, it will tell you.

Yes, booking in advance saves you money. but once you book, you are committed and cannot change your mind without paying extra.

Booking tickets online is a bit more complicated. Try https://www.bahn.com/en/view/index.shtml or https://www.trainline.eu/ or https://loco2.com/

so, would it be best to just wait to book the train when we get there?

Not if you're certain of when you want to travel and your trip is months in the future. There are savings to be had by buying tickets for long trips like that shortly after they go on sale. But the cheapest tickets are non-changeable, so you must be sure of your schedule.

The fast trains occasionally sell out, too, so waiting till the last minute is a bit of a risk in that regard.

Same day direct service...
ECB 86
Dep 13:50 VENEZIA S. LUCIA (Italy)
Arr 20:26 MUENCHEN HBF (Germany)

Book 90 days in advance to secure discount seats. Go to trenitalia ... http://www.trenitalia.com/tcom-en/Purchase/Purchase

You may see Munich listed as Monaco Hbf on Trenitalia. Don't panic, the train station in Monaco (country) is Monte Carlo.

I book my train tickets online in advance on the German Deutsche Bahn website for my Zagreb-Munich trips. They mail you the actual ticket in just a few days to N.America. I would use them rather than the Italian website; they have never made an error. Because I book well in advance, I book a first class ticket - as a senior I get a great deal (you have to look for further details on passengers on the DB website to tell them that). First class is often empty, and much quieter. Train restaurants are great places to watch the mountain valleys and peaks from. Worth a few euros for coffee and food. If you can decide the exact date, order now. Even a slight advance online booking can reduce the prices. This applies to all trains across Europe and the UK - never pay same day fares! When arriving in Munich stay on until the Hauptbahnhof itself. of course. If travelling onward, there is a good info centre in the station.

Just tossing this out there - Have you considered flying? It's one-hour non-stop.

If you have the time, take the train. It's a beautiful trip through Austria and the Brenner Pass.

I took a train a few weeks ago from Innsbruck to Venice and it started in Munich. The train was run by the Austrian Rail System.

Use the German Rail Site, Deutsche Bahn, to find the train you want in terms of schedule and then book it from wherever you allow. The Austrian site is not user friendly. It only cost me 44 Euros for first class and I booked a couple of weeks ahead of time.

There is a single direct train per day, run jointly by Austrian and German railways - the ticket can be bought from them or from Trenitalia. All other travel solutions involve a change in Verona, in which case the Venice-Verona ticket is from Trenitalia and the Verona-Munich from Oebb (Austrian) or DB (German railways).