Very cheap extended weekend escape to Rome from Athens from 29,98 euros with our favorite ryanair.com.
For 0 euros check couchsurfing.org
Enough people to rent a flat? check airbnb.com it might get much cheaper and more cozy from hostels and hotels.
To and from the airport?
Check the official website here: http://www.adr.it/web/aeroporti-di-roma-en-/pax-cia-to-from
If you book early enough you can get better prices with some bus companies.
-Double check your hand luggage size according to the company's limitation!
-Remember to check in online and print your tickets!
-Try to stay close to the center in order to avoid extra travel costs!
-Information about the public transport in Rome can be found here: http://www.atac.roma.it/?lingua=ENG
-Stop looking, start booking and enjoy Roma!!!