Seeing as the main ship of war type for the era was the quinquereme/penteres, it's silly to have trireme as the main ship type. I'm all for just a name change, as the ships didn't change much once the Hellenistic states died off. It's pretty telling there wasn't much naval tech advancement, as the Battle of Actium, some two hundred-ish years after the beginning of the game, was still mostly quinqueremes with a few bigger ones mixed in.
The only division I could see would be two types of ships, heavies and lights, with biremes/triremes/quadriremes/lembi/whatever else you want to put in here being lights and anything bigger being heavies.
Mechanics wise, I'd give lighter ships higher speed, less health, less manpower requirements, less naval power, some sort of stealth or blockade running stat (perhaps just the higher speed would help this). Heavies would just be the opposite, lower speed, higher everything else.
The thing is, I don't see the point, as, unless they're going to add shallows and blockade running, the lighter ships will have no purpose other than pirate hunting.