use bullets 40 grain to 55 grain. If you are reloading, what brands of powder are available in Italy? If not, then purchase a few types of ammunition and see what shoots best for your gun.
22-250 is great (explosive!!) for small non-game animals like squirrels, ground hogs, crows, coyotes, etc. Its not so great for deer because the bullets in 22 caliber usually have a light jacket, not designed for penetration.
However, if you make a head shot on a deer, it will work fine. Just don't plan on keeping the head!