Kitchens in Italy are...interesting. Italians like to "take their kitchen" when they move. Which means that typically when you look at an apartment to rent there is nothing there but some water pipes where you would put your sink. I had a hard time wrapping my head around this. I still have a hard time with it. So if you end up in private housing you have to figure out what to do with your kitchen (arrange your contract so the landlord puts a kitchen in or make a big IKEA run...)
If you're in goverment housing like me, it is taken care of. It's not amazing, but you do have a fridge, sink, dishwasher and maybe some counter space. Below is a picture of my set up. The walls are just outside the edges of this picture. The only other thing you don't see in this photo is my fridge which is on the opposite wall. So as far as counter space/storage space what you see is all I've got.
This is definitely something to consider when deciding what to bring over with you...of course everyone's situation is different. But I can tell you that most people here complain about their kitchens.