An INterrail Global Pass 2nd class costs a fair amount but is valid for 10 days - see here:

Italian Railways - Official UK Site - Information on Italian Rail Tickets and Passes, timetable, maps and live bookings on the whole network at low prices

Sleeper compartments might cost extra [in fact I am sure they do] but its an adventure your going on not a holiday!

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sigged by Firebird of Stratics! Thanks!