What jacket to wear

Are you from Miami or Fairbanks?

Some would find upper 50s 'frigid;, others would find it mild.

Plan to be out a lot at night when its likely to be near only 40F?

Nighttime temperatures in Venice are likely to be down in the 30s F at that time of year, and it could feel quite raw. I find even 50 F miserable if I get wet, so I'd want good rain protection. I ran into about 40 F and wet in Spain early last April, and I was very glad I was traveling with merino-wool long johns (intended for Scotland) nylon slacks that did a decent job of shedding water, a fleece jacket, a totally waterproof jacket, waterproof shoes and an umbrella. It wasn't fun, but I wasn't really cold. But I am a cold-natured female; you might need less.

Two tings:
1) look at weather forecasts
2) look at these Live Cams on Youtube - look in the AM, when it's day time there.

Venice
Rolling cam - 4? cameras
https://youtu.be/ph1vpnYIxJk

Florence
https://www.youtube.com/watch?v=ditXBG3sH14
lots of people wearing shorts Friday

Rome
https://www.youtube.com/watch?v=A_MzGDs3JHE&t=106s

You can look at weather forecasts, but likely they will range from mid-30’s at night in Venice to mid 50’s during the day. In any case you need an outer layer of good rain gear. And an insulating layer to wear underneath when it is cold. I would not take a heavy top coat; I would just take a good rain jacket and layers to put underneath when cold. That is what we will do when going two weeks from now.

I was in Venice in late October/early November and found that my Columbia long coat with the "Omni Hheat" lining was quite comfortable, whether it was raining (pouring, actually), windy, sunny or whatever. When we went further south, the coat was not too heavy in the warmer weather and I could roll it up and stuff into a backpack or tote when it was too warm to wear. Best advice is to wear layers that you can load on and peel off as the temperature changes. Enjoy your visit!