Short trip

3 cities in 3 days? Yikes! I'd rather go straight to Florence from the airport and have 3 nice days in Florence. You can get a flight from Florence to Munich on Air Dolomiti/Lufthansa for about 100 EUR each, or, if you feel adventurous, take the Nightjet sleeper train.

Agree with Sam. Pick one of those cities (or some other place along the way) and spend all your pre-Munich time there. Venice will cost you extra train time, so really Rome or Florence would be better. Otherwise, you're going to be doing little besides bouncing between train stations/airports and hotels.

Another vote for one place. 3 nights is two full days; one night is no days really. Neither Rome nor Florence is worth half a day -- 3 nights/two full days is quite minimal to get anything out of them. So I'd stay in Rome, see ancient Rome and visit the Vatican, then train or fly to Munich. Or go straight to Venice or Florence and spent your time there and then fly to Munich. The day a city plan is all logistics with no being there.

Another 'pick one' vote

one or the other, not all three, certainly, and not even two. Pick one.

you will be on the train the entire trip. Another vote for one place...Florence itself and the area has enough to keep you busy!