We can't understand your "remove" o rimuovere with reference with an house, maybe you're using a wrong verb?
Do you want to buy or rent a House?
Prices may vary a lot!!!!
Roma and Milano are very expensive a one-roomed flat can cost from 1000-1200 each month + expenses for light, running expenses, etc.
Other cities prices may vary from 500 (south of italy, and more poor regions) from 900 for a larger apartment each month + expenses for light, running expenses, etc.
Obviously if you want to live in rough district prices are lower but it's not a good idea for a nice girl from russia :)
As for buy in Italy prices vary a lot!
Italy is a varied country so you'd be more precise!