Italy Train Reservations with EuroRail Pass? Do I need to make them?

No worries about 1st class. None of the route you listed are regional trains except when you go to Basel based on a test booking.

Use this site for your Italian rail seat reservations.
https://www.eurail.com/en/reservations/reservation-self-service
You need reservations for
Rome To Florence
Florence To Venice each way
Florence to Basel (you change in Milan)

You need reservations for:
Basel to Munich
Here is the site to make them
https://reservations.eurail.com/
I've never used a a rail pass but the site explains it all.

Seat reservations are mandatory on all high speed trains and cost 10 € per person, per train. You can get all the reservations you want at once, either on-line on trenitalia.com/tcom-en or at the first station.
Italian trains rarely sell out in second class, n-e-v-e-r in first.

Note that with a global pass you can freely get on the slow Regionale trains, the locals used by commuters and students.

Italotreno, the new US company running high speed trains in Italy does not accept passes.

If your plans are set for when you want to travel from place to place, you should go ahead and make your reservations.

Remember to activate your Eurail Passes either the day before or day of your first train ride, depending on the time your first train departs. Google "where to activate Eurail Pass at [name of station]".

Have a great trip!

Glad you're making the best of your "Eurail" buyer's remorse situation. Italy is one of the cheapest countries to travel with point to point tickets.

I don't know that you would be required to have a reservation on the DB trains from Basel to Munich, with at least one change. Heading north from Basel it will be either an ICE or IC and while they sometimes get a bit busy I've never needed a reservation.

In Germany, reservations are possible, and with a group of 5 might be a good idea but are not required.

In Switzerland reservations are the exception and many trains don't offer them.

In Italy every leg of every train which is higher than R or RV - that's all of the faster ones - require reservations, included with normal tickets but €10 per leg per person for pass holders. The reason I mention that is that you need to know that for the Florence to Basel day you will be changing trains in Milan so you need to buy reservations for the Florence - Milan leg and then another set for the Milan - Basel (or wherever you break the journey or change trains in Switzerland) leg.

Reservations are definitely not required for trains from Basel to Munich (unless you choose a leg by bus), or pretty much anywhere else in Switzerland and Germany. By the way, why Basel? Are you not going to any mountain destinations in Switzerland?

Our web site has recent and accurate information on this topic. See the individual country pages, e.g., for Italy and Switzerland:

https://www.ricksteves.com/travel-tips/transportation/trains/italy-rail-passes

https://www.ricksteves.com/travel-tips/transportation/trains/switzerland-rail-passes

If you did not buy the pass directly from Eurail.com, then you cannot make reservations through the links that Jazz+ included. With our Rail Europe reservation link, it doesn't matter where you bought the pass. Reservations are also easy enough to buy from a ticket window or ticket machine in Italy (fare category may say "Global Pass") and you could buy a couple when you have the pass activated at your first station.

The German link for train schedules is usually the most accurate way to see types of trains on your route and whether they require seat assignments before boarding. However, for the past year, they have NOT accurately reflected the need for reservations in Italy. If you view details of for fast trains in Italy, they show the note "Global Price," which actually does mean reservation required (included at time of ticket purchase), but is not at all clear for the average consumer. I've asked them to change that.

Thank you all very much for your replies. What is the best way to check train times for the Italian trains? I hear they can fluctuate. Also, in response to your question about Basel - we are going there because our friends recently moved there and we are going to visit and stay with them. We will be in Europe for a total of 2 months and it was really hard to narrow down the locations!

To only look up Italian rail schedules try

http://www.trenitalia.com/

When using trenitalia.com you have to use the Italian spelling for the names of the cities

or

https://www.bahn.com/en/view/index.shtml