Yes, it's very similar for me as well - also in terms of having being exposed to classic mythology at a very young age :)
I share the same view: the main element is keeping the story broadly in line with the original myths, in terms of themes, tropes, and narrative approach. At the same time, I want the players to have different options available, and to be required to make a "moral" choice of some kind - I want them to be able to take either side in the conflict they are presented with, and ideally to also have "third" and "fourth" options to solve it creatively.
And I agree about landscapes, references to local trees, plants, agricultural practices, etc. really help creating the right Mediterranean atmosphere. Greek and especially Southern Italian landscapes are my main inspiration from this point of view.