How to decide what writing sample to include in a phd application?
I think most of the other advice given above is sound. Let me add two things that I've noticed in reading work by first and second year european grad students who are transitioning into the US system. 

The paper you send for a writing sample needs to have a clearly identified thesis in the first or second paragraph of the paper. If you can't think of something better write, "In this paper I am arguing that . . . " Many of my european colleagues want the thesis to emerge slowly, reflectively, at the very end of the paper after all the scholarly qualifications and so on have been properly put forward. Don't do that for an American audience. Tell us up front what you are trying to say.

Second, hire a native english speaker to proofread your paper for you and really work on grammar, spelling, idiom, and style. Writing well is really hard and it's the primary job you'll have as an academic. (Your writing in the question is excellent. I'm just saying having somebody who really knows English double-check it.)  Coming from Italy, I don't think most admissions committees are going to hold language against you constantly. It is easy to create a subconscious impression of carelessness with casual mistakes in the language. For something as important as getting into a good grad school it's worth spending some money to get this part right.

Good luck.