Eurail or German Rail

You booked 1 night in Berlin? This is far too less for Berlin imo compared to over 10 hours train trave time from / to. Just as an example: The tourist website comes up with a 3-day itinerary not to miss top sights. So, it is doable but do you really want to spend so much time in trains compared to time at destination?

European destinations need time for experiencing which is a big difference to a lot of US or Asian destinations. 1-night city hopping will bring you an extremely high-level impression only.

To anwer your question: use Deutsche Bahn ticketing for the legs to / from / in Germany.

You aren't flying home out of Florence - correct? So you have an additional travel leg at the end.

A German Rail pass is valid for 3 full legs of your trip - Berlin - Nuremberg, N'berg - Munich, Munich - Venice (on certain trains.) It could also be used in part for your first leg between the Dutch border and Berlin - but you would also need a normal ticket from A'dam to the border also. 3-day pass for two = €292 at DB. It's only €22 more for the 4-day pass (€314.) (Note that there will likely be a spring special promotion for the GRP in certain versions sometime after Jan.31. That sale has happened for the last several years.)

Alternatively, at the DB site, A'dam - Berlin, Berlin - Nuremberg, Nuremberg - Munich, and Munich - Venice can all be pre-purchased at discount rates as individual tickets. These are "saver fares" or "Sparpreise" in German, and there are certain conditions. Prices rise with time as tickets sell, so "buy now" is the adage for the best prices.

The German Rail pass is a good bit less trouble than individual tickets and worth some small additional cost for the convenience. Also, there's no pressure to commit to an itinerary fully or to purchase the GRP right now - you can do that much later, or even in Germany.

Use this page to find schedules for ALL your journeys - the ones in Italy too - and to find saver fare tickets for your dates:
https://reiseauskunft.bahn.de//bin/query.exe/en

The last 3 train rides you mention in Italy cannot be booked at DB. You might look into a flight for Venice to Napoli. Read up on the options at Mr Train Guru's site:
https://www.seat61.com/Italy-trains.htm

If you need an extra ticket from A'dam to the German border (as you would with the GRP scheme) you can buy it at the station in A'dam or prepurchase it at either the Dutch Railways site - www.ns.nl - or perhaps at DB.

BTW I completely agree with the previous post. Short stays like the ones you've planned are almost worthless. If you have insufficient time to see all these places properly, perhaps just take the train from A'dam to ONE city - Munich? And stay for several days. (You could do a day trip to Nuremberg and back from there perhaps, if you had enough time.) Then move on to Venice.

Eurail or German Rail
do we get Eurail or use the German Rail,
Again, Eurail or Italian trains?

Forgive me if I am wrong, but it sounds like you are under the common misconception that Eurail runs a rail service. There is no such thing as a Eurail train.
Eurail is a reseller in North America that markets passes which are valid on trains run by various railway companies in Europe.

Unless you are doing a lot of travel (and I don't think you are), the cheapest way to travel by train is to buy tickets direct from the operator, especially in Italy where tickets are cheaper than other countries. And even with a pass, you need to pay a surcharge to travel on many long distance trains, for example in Italy,

The best way to check on train times and buy tickets is direct from the companies running the trains.
In Germany, the main national railway company is DB: https://www.bahn.com/en/view/index.shtml
In Italy it is Trenitalia: https://www.trenitalia.com/tcom-en

For more impartial information on passes read here, especially the section "Should you buy a Eurail pass or point-to-point tickets?": https://www.seat61.com/Railpass-and-Eurail-pass-guide.htm

And, no one night stops, you will have no time to see anything. Minimum 2 nights, better 3.

Point-to-point tickets, when bought in advance, will be cheaper than a rail pass. For your travelling in and from Germany (including the trip to Venice) such advance-bought tickets will come around EUR 100 per person (EUR 120 counting from Amsterdam, which is not included in the German rail pass). I assume similar will be true for Italy.
When buying separate tickets, you can at the same time make your seat reservation. It is not mandatory on German trains, but for a few euros it gives you the peace of mind to be sure of your seat.

I'm assuming by "Eurail", you're referring to a Rail Pass. For the Italian portion of your trip, I'd suggest using locally purchased tickets, as a Rail Pass is rarely cost effective for travel in Italy. Tickets for Regionale trains are very cheap, however if you buy these at local stations, DON'T forget to validate before boarding the train on the day of travel or you'll risk hefty fines, which will be collected on the spot.

You can save money with advance purchase tickets for the express trains (Freccia and Intercity), but tickets for these come with compulsory seat reservations that are specific to train, date and departure time, so you MUST be willing to commit to a specific departure when you buy the tickets. Tickets for these trains do not have to be validated. Be sure that the train you're boarding is the one listed on your ticket, as there are also hefty fines for boarding the wrong train.

If you want to buy advance tickets for trains either in Germany or Italy, you might try www.trainline.eu, which sells tickets for the same price as the rail networks. They sell tickets for both major rail networks in Italy (Trenitalia and Italo).

When we traveled to Germany and Austria we chose the two-country rail pass from Eurail. This year since we’re staying Germany, we chose the German rail. Both times we bought the flexible pass (x number of days to be used non-consecutively). They both look and operate the same. They were an incredible value compared to individual ticket costs. The convenience and peace of mind of always having a ticket (like when we missed our stop in Baden-Baden and had to travel back on a different train) was priceless.
So, if this was my decision, I’d count my travel days in each Germany and “other” and see if it was cheaper to do a Flex Pass total from Eurail or to split it to a small Eurail and a German one.
I do think that someone nailed it when they suggested that there might be some confusion about Eurail being an actual rail system company. It’s easy to do! It’s just a company that can sell you a pass that will cover many companies.
I disagree that it would be cheaper to purchase individual tickets especially considering the distance you’re traveling.
Lastly, (unsolicited advice here,) learn to reserve ICE trains. You don’t want to stand in the stairwell next to the broken WC for an hour while motion sick. Just saying...

Keep in mind that if you get the discounted tickets, they are, as correctly pointed out, train specific and departure time specific, not one or two hrs later. It is specifically indicated on the ticket which you print out. Do anything different, you pay all over again, ie no credit given for the amount you already paid. Basically, it comes down to savings over flexibility.

If you're willing to sacrifice flexibility for savings, then get that type of ticket, knowing that you've locked yourself in. Conversely, if the savings is irrelevant, not worth bothering with, then get the pass. I use both, the rail pass and discounted tickets, all depends on your traveling style.

The best site to learn about train travel in Europe, including various pass options is
man in seat 61

They were an incredible value compared to individual ticket costs.

This is interesting to me. I'd love to know your routes and how much you saved! Also, what website did you use to compare pass costs with individual ticket costs? Thanks!

They were an incredible value compared to individual ticket costs

As a rule, that's true only f you make a rather long distance ride every day. You can calculate that yourself by searching for saver fare tickets on www.bahn.com (bookable six months out, pricews increasing and never decreasing).

And with regard to the putative flexibility of a pass ...

Lastly, (unsolicited advice here,) learn to reserve ICE trains. You don’t want to stand in the stairwell next to the broken WC for an hour while motion sick.

.. as soon as you follow that advice (I think you should), your flexibility will be lost.