Can anyone please Help with best order of itinerary by train

For Amsterdam to Munich, I would scope out the "Nightjet" sleeper car (or fly). I am less familiar with the rest of your northern plan, but can help with the Italy part. Indeed it is best to move north to south, but there is nothing you can do about that long slog from Venice to CT. Many (myself included) advise picking either Cinque Terre or the Amalfi Coast (the other side from Sorrento), as they both offer something similar--scenic coastal hiking. Also, October can be iffy for CT weather-wise, but I would risk it for the Amalfi area as there are many alternative sites that are not weather dependent.
See schedules on the Trenitalia and Italotren websites.
Between Naples and Sorrento, it is commuter train.

Looks like a great trip! The outlier geographically in your list is Switzerland. I am guessing your are going there for a mountain setting? One idea would be to do the mountain thing instead in Austria or Italy (the Dolomites). This would also save on cost, as Switzerland is super expensive. Just an idea....

Good call, Bob--since you mentioned staying in hostels this is a strong consideration, as Switzerland is indeed very expensive (and Rome and Venice are no slouch in the accommodation pricing either)! That could save you some time as well.

I would skip Cinque Terre and visit The Amalfi Coast not far from Sorrento. Also, visit Capri and Pompeii.

You left out Florence, you shouldn't skip that wonderful city.

Regarding Switzerland, probably the most expensive country in Europe, Lucerne is a must see.

For me personally, I would fly from Amsterdam to Munich (even the fast train is about 8 hours), and I would leave out Switzerland as it's going a bit out of the way. I agree with others if you want to see mountain scenery you can see the Alps in Austria or the Dolomites. I think the rest makes sense.

We went to Cinque Terre in very early November and it did rain quite a bit- the weather might be similar in mid October.

You are smart going from north to south weather-wise also. I too would skip Cinque Terra and go to the Amalfi coast/Sorrento/Naples, visiting Pompeii as well. A day trip to Capri, if a visit to the Blue Grotto is possible (sea and weather-wise) would be nice. That time of year would be less busy, and no matter what people say about the crowds, the Grotto is very beautiful and unique. I treasure my memory of it. Munich is one of my favorite cities. The Austrian Alps are great as are the Dolomites (Italian). Personally I would skip Switzerland due to the expense, plus Switzerland isn't the only place that has beautiful Alpine settings and scenery. On the way from Venice I would definitely stop for 2 days (3 nights) in Florence, then Rome and South toward Sorrento.
By the way, I have never been, but what I read on this forum is that the Eagle's Nest tour isn't so great. See what you can find by putting that in the search bar on the German section of the forum. I could be wrong.
You will have some long/long-ish train rides, but take them as a bit of down time to relax and enjoy the scenery, read, write postcards/journal, doze.......
My one long train ride back in 1974 was through the Brenner pass, going from Verona to Vienna. (Can't remember the major Italian station we left from). It was a magnificent ride!

Good luck with your planning. If it is this Sept./Oct. you should nail things down pretty soon. The days of finding lodging, even at hostels, on the fly, are pretty much in the past. Ditto some of the train rides.

Thank you all so much. That was exactly what we needed!! I will share this with my daughter tonight and I believe we can finalize our plans. Definitely more excited than stressed now!!