Transfer services from Piraeus Port to Athens Airport

Most economical - the metro, or the x96 bus.

Best? Kind of depends on things like how much luggage you're carrying, timing of
your journey, etc.

If you are arriving on a cruise ship, do they not offer a transfer option?

If you are arriving by ferry from an island, be sure you give yourself plenty of time so you do not miss your flight.

Which is more important, 'best' or 'economical'? "Best" and "Economical" usually occupy opposite ends of the cost spectrum. It's a subjective judgement of where on the range your sweet spot is.

How many in your party?

If you would like personalized service. Welcome pickups is a good option. Compare their prices with transfers offered by the cruise company transfer.

I've used Welcome Pickups twice in Athens. Both drivers were on time, spoke English and gave great service. I'd use them again.