N. B. If you want to take the subway: you need first to get to the subway terminal of line 1. When you change to line 3 (airport line): not all trains are going to the airport and there are no special trains for the airport traffic. So all airports trains are used by normal passengers as well. It could be that you have upto the city limits of Athens all rush-hour traffic with you in the same train. It's no fun.
Therefore we took the airport bus from SYNTAGMA square. Because there was the terminal and we could enough seats and space for the baggage.
If you are not in hurry and want to see something from Athens incl. free of charge view of Akropolis:
Take the cab to Peace & Friendship Stadium.
Take the tram to Syntagma (you see some of the former Olympic Games stadiums), Akropolis and Parliament building enroute.
Take the bus to Airport.
Free of charge-sightseeing!
You will always enter the tram and bus at their terminal so enough seats and space too choose.