I've used the Metro numerous times from the airport to Central Athens and to Piraeus.
I never had any issues with safety whether pick pockets, bag snatchers or any other bad experience.
At the airport you'll have ample selection of seats as it's near the start of the run but as you get closer to Athens at each stop more and more people get on and by the time you get to Monistiraki or Syntagma it's very crowded.
That's when you need to be careful about your belongings as it's elbow-to-elbow getting off and heading for the exits.
I've also taken the bus which is safer, cheaper but does take more time.
If you are concerned about safety then a private transfer is your best option as it's door-to-door service but albeit more expensive.
If there is more than two people needing a transfer then it may be more cost effective and more peace of mind to go that way.