Greek store etiquette:

I've been paying for stuff in Greece since '99, in 13 trips, and i've never been aware of any payment etiquette, which seems to indicate that there isn't anything special in Greece. As I recall, and people will correct me if I'm wrong, but that business about not touching the hand of a store clerk may be more of an Asian sensitivity. I remember reading about Americans in US stores owned/run by Koreans, who mistakenly felt the staff was stand-offish, when it was just this custom of no hand-touching during purchase.

Does the customer hand coins/cash directly to a Greek store clerk or place it on the counter?

No knowledge of cultural norms, but from a logic standpoint, if the clerk puts a hand out when you are passing out the payment, hand it to them, otherwise set it on the counter. If using coins, the counter may be the better place to make counting easier.

When we were in Greece , I did nothing special and the shopkeeper always seemed happy to have made a sale.

In places where it is considered rude (or even undesirable) to hand money directly to a cashier (as varied as Italy and Japan), there will always be a tray to put the money on.

So, that's how I determine it. If there's a tray, I use it; if not, I don't worry about it.