SIM card : can I buy one in Amsterdam that will also work in Italy?

Yes.

The EU introduced free roaming among member countries a few years ago, so you won't pay any more to use a SIM in Italy that you bought in the Netherlands than if you had bought it in Italy.

I have been to Amsterdam a few times, but not for a few years. I don't know if there is a place to buy a SIM at the airport or not - I'd guess so.

Curiously, though, I have been using a Dutch Vodafone SIM card for years, since 2017 - and never used it in the Netherlands. I bought it on eBay (can't anymore I guess). I have kept it alive ever since and used it on several trips - twice in Italy, also Slovenia, France, Spain, and Portugal. I don't need need to make local calls in Europe with it - I mostly want it for the mobile data, and it has worked great for that. I can top it up online on their website.

If it's anything like CDG, you won't need an actual phone store — in French airports and train stations, you can always buy SIM cards in press stores, which have the brand name Relay in France. My guess is that AMS has the same kind of stores (maybe not the same brand, of course) also selling everything including SIM cards.

You can also get an eSIM data plan that will cover multiple countries. It's easier than having to insert your SIM card, and you can switch back and forth between the eSIM and your regular phone in a few seconds. There are several recent posts about this if you scroll through the Technology Tips forum.

Thank you.
I’ll see what’s available at AMS, then if it doesn’t suit me, I’ll get one in Italy.

We have T Mobile, and they have relatively inexpensive European plans--including everything. The phone works just like it does at home--including getting Medicare spam calls. Our 3 1/2 year old granddaughter used her mother's speed dial @ 3:00 a.m. to call our home phone--and it rang in Budapest and woke us up.

We cancel the T Mobile international plan upon arriving home. No SIMS cards needed. T Mobile is owned by Deutsch Telecom.

Yes your SIM card should work all ove Europe. Ours did.Bought in UK and used it in Italy too.

Vodafone UK still offers EU roaming on it’s pay as you go plans. It’s probably best to check the details of any provider to make sure it suits your needs.

https://www.vodafone.co.uk/mobile/best-sim-only-deals/pay-as-you-go-sim?icmp=uk~1consumer~topnav~1shop~2simonly~2payasyougo_sim&linkpos=topnav~1~1~2~2

These Vodafone prepaid SIMs also seem to cover roaming in Switzerland as well, so even some non-EU countries are covered.