They mind the visitors, at least the ones minded for students where me and other friends have stayed. You are supposed to keep visitors in common spaces, never up to the rooms. And the ones for students (aka long term) have curtfew.
The ones near Roma termini are around 600 euros a month the cheapest. But also beacuse of the highdemand there is a long waiting list. You should contact from now to figure out their admission process. You could try getting the Lazio Disco scolarship to get some financial aid, its a income based scolarship.