<span>Religion, at that time, was governed by the State. In such, the government controlled all aspects of religious life and what sorts of materials would pass muster as being "proper" and what viewpoints would be considered "non-threatening" to the health of the nation. Any belief systems that were outside of this were considered verboten.</span>
There is not right or wrong answer for these questions. I would have dinner with Athena the God of wisdom and military victory (Parents are Zeus and Métis) because she would be interesting to sit down and to chat with over her victories and accomplishments in life.
I would say the Gods of inspiration Muse would be suited for president because she would aspire everyone to be better as a person.