A trireme is only a good choice in a military campaign. Trireme are pure warships, historically they were the 'capital ship' for centuries. The need to pay a crew of nearly 200 makes them totally uneconomic for trading and the need to feed that crew makes them a poor choice for most exploring missions.
I recommend two historical novels by 'H.N. Turteltaub', (a pen name for Harry Turtledove, a trained historian turned fantasy author) - 'Over the Wine-Dark Sea' and 'The Gryphon's Skull'. They describe voyages by a pair of brothers from Rhodes in their fast merchant ship, in the interesting times just after Alexander's death. The stories have almost no magical elements but they give such a good picture of their period that they still have the feel of taking place in a very different world from our own.
Andrew
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