Best Way From Rome to athens?

It will probably be cheapest to fly, best because it's the fastest. By the time you pay for transit to one of the Italina ferry ports, pay for your ferry across to Greece, and pay for your bus or train to Athens, PLUS pay for meals along the way, most likely you will have spent about the same amount of money as you would for a plane ticket, BUT you will have spent around 24-30 hours in the process. What's more important, saving time or saving money?