If you don't want to change phone # from country to country, get a SIM card from the country were you'll spend most time. If that's Italy, Í'd say all operators here will work everywhere in EU: Vodafone, TIM, Wind, Tre. TIM and Vodafone will have the best coverage in Italy, so you probably want to get those.
I'g get a SIM card and then charge it as needed. In Italy is just like in Germany, you can charge it virtyally everywhere but, most conveniently, on line with your credit card.

There are zillions, and constantly changing, and quite confusing plans you can pick from, and I can't recommend any of those specifically because tomorrow they'll have a different name and will change fees slightly. Just stop in a shop and get whatever plan costs you less when calling/being called from abroad. That's it. Also, unless you spend in EU months, you won't probably notice any significant difference in cost, after all.

I actually happen to have a Vodafone working SIM card which I am not using (it used to be in my dismissed car sat system), so I'd be happy to let you have that, even though I'm not sure how to work this out. Let me know if interested.

Phones: Nokia2323. It's the most basic one, and you can find it at 30 euros in shops or on line. Possibly less. It works and hopefully won't break open if you drop it. And software won't be that bad as similarly priced competitors.

I always used my phone(s) when in the States, in the last 10 years, though. Most GSM phones are tri-band since a long ago: 900 (EU), 1800 (EU), and 1900 (US) MHz. So, unless they are carrier-locked, a phone you get in Canada should work here too.

Operators in EU will have partners in other EU countries which will give you better fees.
Wind in Italy = Orange in France and UK.
France Telecom = TIM in Italy = BT in UK (I think)
Vodafone is in all the above countries.