A Doppia has two beds in it, a matrimoniale has one double bed in it. Private baths are generally more expensive. Sites are generally noisy but modern. Prices often include breakfast. However, curfews, lockouts, and remote locations are sometimes an inconvenience.
Prices can be exorbitant.
Groups may have the advantage in getting reservations. The price set by the state should be posted on the room's door. Accomodations in Bologna tend to be scarce and relatively pricey. Accomodations are plentiful in Milan but peak season is practically year- round, so make reservations ahead of time if possible. Restaurants Italian food is well worth a bit of indulgence.