David be sure you specify to Welcome Pickups that you have FOUR adults, each with a "LAarge" suitcase. The standard vehicle for both taxi companies AND car services is a 4-door mercedes. It will be difficult to fit 3 n the back seat of even this capacious car, lunless 2 are small size women, and men in the party are under 200 pounds. Also, I've found that while this size of car can (barely) wedge in 4 20 or 2l" "rollaboard" suitcases, it cannoot accommodat eht large (25"?) bags required for cruises, with all that dress-up. In addition, all 4 of you wouold have to hold your "daybags/Knapsacks" on your laps. If you give the dimensions of your bags, a car-service probably will charge you for a mini-van or at least a RV. If that is fine witih you, then go ahead... just know what to expect.
If you'd rather take public transit without crowds, rush or any steps, you have a wonderful resource only a few hundred feet away from the front Door of Grand Bretagne, lucky you! It's x95 KTEL EXpress bus to ATH airport... and it stops at the far uphill corner of Syntagma Square from you, at the curb at the top of OThonos Street. You can see it from the hotel door or windows. There's a kiosk where you buy your ticket (€6) and you step right from SIdewalk into bus... modern, air-conditioned, comfortable, goes about every 35 minutes; a timetable is on the sign. Takes same road as taxi or cars service, in mid-day, about same travel tme, under an hour. Only about 2 stops... so, No pickpocketing or pushing. You take your baggage on board, and pile it in a central "pen" right next to you. When you reach airport, it's terminus, take your sweet time getting off, and 5 feet away is door 5 into main room of Airport.
IF you say you've seen posts on how easy this is, you must have missed mine or you would not have questions. I post this info every week, and it always seems to be met with surprise, as if it's something new ... yet I've used this for at least 8 of my 13 Trips to Greece i nthe past 25 years.