The three great Greek tragedians (Sophocles, Euripides and Aeschylus) would have to be contenders for the best.
I suppose most well-known would probably be Homer or Plato/Aristotle from Greece whilst from Rome it would probably be the Caesars who wrote extensively (Marcus Aurelius/Julius Caesar).
Then there are the historians like Herodotus, Plutarch and Livy.