Uhm.. As far as my nation's history with ship design and building, I think I have to go back to Venice when it still was a major sea power in the 15th-16th century.
At the time, the most famous (and successful) class of ship was the
Galley, a long and narrow trade vessel with large sails, capable of reaching very high speeds. When deprived of cargo, it became an effective warship thanks to the multiple rows of well.. rowers that gave the ship superior maneuverability. It generally carried a large crew complement for boarding actions, a small number of guns where available, and a bronze beak for sinking enemy warships in close combat.
The other ship class that springs to my mind is the
Galleass, a large warship employed during the famous battle of Lepanto, where the Turks mistook a number of these vessels for supply ships and got blown to smithereens. It was basically the opposite of a galley, with a large,fat and shallow hull, and mounted a large number of high-caliber guns. It's a step between the galley and the "true" galleons of the 17th century.
Also popular in later centuries was the
Brigantine, a small and nimble vessel mainly used to counter piracy (or practice it, depending on whose side you were on
) . A small atoll near the Island of Ponza, in Italy, is called
Cala Brigantino , the Brigantine Cove, because a Sardinian Navy Brigantine used to station there in the mid 1800s against the Berber pirates.
It wouldn't be of much help to go back at the time of the Romans, I'm afraid. Pragmatists to the very core, the Romans simply classified their warships based on the number or rows of oarsmen. From a Bireme (2 rows) to a Quinquireme (5 rows). Very archaic-sounding and not much suited to a sci-fi game in my opinion.
Italic, and Mediterranean, vessels have always tended to be very fast and moderate in size, since they never had to deal with the harsh weather of the ocean. North African traders and corsairs employed a particular ship called the
Xebec, equipped with a set of triangular sails and capable of high speeds.
Also, a favorite of the time was the
Polacca or
Polacre, a trade vessel with triangular sails.
I can' think of any more right now, also because it's quite difficult to find information about ship designs that don't require you to be a shipwright to understand. Modern ship classes are pretty much standard all over the world, especially military ones.
While I'm at it, I'd like to point out a (very small, very technical) mistake in on of the contracts, namely the "Federation Battlecruiser". One of the requests was for the ship to have a high shield value. Historically, Battlecruisers were an intermediate class between heavy Cruisers and Battleships, with very high top speeds and battleship-size armaments but very little armor. The contract for a Battlecruiser should therefore require high top speeds instead of high protection values.... Or you could just ignore this technical junk and keep the name on the basis that it sounds cool and reminds of Starcraft