Nice collection! Just a few tweaks and comments:
Recon:
The Liburnian was such a quintessential Pirate craft throughout the Classical period that it cries out to be a specific Barbarian Boat. Lembos, on the other hand, was a generic (Greek - in Latin it is Lembus) term for 'any light warship' - specifically, lighter than any polyreme, including the Trireme, so a nice term for the lighter recon types we want to depict.
Melee:
The Quadrireme was the main warship of the eastern Med for less than 70 years, and as a 'melee' ship was completely outclassed by the Quinquereme, which could carry more marines (120 to 75) and was more stable, better protected, and had a higher deck giving a tactical advantage in boarding actions. The Quinquereme was the definitive Melee Warship, used extensively by Rome, Carthage, and the Hellenistic Greek states for 400 years (399 BCE to Augustus' time).
The Galleass was primarily a design to mount a gun deck above a rowing deck of oarsmen, providing relatively heavy cannon broadside with the use of either oars or sails for propulsion. It's a bad choice for a Melee ship, then, because it's metier was firepower - and that's how they were used in their most famous action at Lepanto in 1571 CE. The Carrack, on the other hand, was a true 'melee' ship from the late 14th century (1380 - 1410: first illustrations and mentions). Examples from the 16th century carried only 5 - 22 'anti-ship' cannon, but also 64 - 79 'anti-personnel' swivel or large hackbuss-type guns and large contingents of troops to board and take enemy ships: classic Melee Tactics.
Ranged:
The larger-than-Quinquereme Polyremes (Deciremes, Heptiremes, Octaremes, etc) all are shown with towers fore and aft for missile troops and were stable enough platforms to mount catapults on them for siege work against coastal cities, so a good choice for the Classical Ranged Ship.
Instead of the Carrack, however (see above), the two better candidates for a Ranged ship are the Cog (Medieval: 13th - 14th centuries) or the Galleon (mid-16th century). From at least the early 14th century the Cog mounted towers for missile troops fore and aft and at Sluys (1340 CE) English Cogs swept the decks of the French galleys with arrow fire, turning the battle into a massacre. On the other hand, the Galleon hull from 1530 CE on was the first hull designed from the start to carry large 'ship killing' cannon and the 'race-built galleon' developed in England later in the same century was the hull that developed into the Ship of the Line after the middle of the 17th century.
"Missile" ships:
The terms Missile Frigate, Missile Destroyer and Missile Cruiser are essentially interchangeable. The Ticonderoga Class Missile Cruisers are smaller than later Missile Destroyers and ships and classes of ships have been reclassified constantly for the past 30 years. The only distinct type is the (Missile) Corvette, a much smaller ship which, at east in Swedish service, uses a collection of stealth techniques to be invisible or nearly so while carrying a formidable array of anti-ship, anti-submarine, anti-aircraft missile systems. This would make a good alternative 'Recon' type for the Information Era, complete with a submarine-like ability to be invisible unless you are adjacent to it.
What happened to anything bigger to Triremes after the Republic of Rome, and later Roman Empire ruled the entire Mediterranean sea as well as North Atlantics? After the end of Roman Civil War which happened after Iulius Caesar is murdered by mass stabbings in Senate. and ended few decades before Jesus Christ was born? Roman Historian (or so) cited that much of Roman Naval Might joined wrong sides (Marcus Antonius maybe? a person who dated Cleopatra VII and ALMOST going to be the Pharaoh of Egypt. again this is not what Republic is pleased) and when the Mark is defeated, so gone a large portion of navy sided with him. What's left to Octavius is a fleet of smaller warships like Moners (the likes of Lembos and Liburnia. Romans also use this term for their lightweight warships). The other reason is that with Rome became absolute ruler of Mediterranean and North Atlantic. and there's no rivals capable to do bigger warships so the needs to build anything bigger with more crews than trirers are diminished. (no longer worths investments and maintenance.). The late Roman Imperial Fleet consisted mainly of Biremes and Triremes, and the design philosophy did changed as well... Dromons and Chelandes which became Byzantine premier warships are considered LARGE by Late Roman and even Medieval Standard and later formed a basis of the later evolutions of galleys (Italian Galea Grossa, or 'Sweeps Galley'), to the Late Republic era however, these are considered SMALL.
I'm not including Nemi pleasure ship. which.. too bad a WW2 victim presumably to either Allied bombings or Fascist Italian arson to deny Allies a prize. it is surely superheavy polyreme but a peasure boat and not battleship (Polyremes are indeed BBs of the Classical Era).
In Civ6 Terms. (Modding only)...
1. What are better candidates for 'Melee' ships and 'Ranged' ships in
classical era?
A. Lembos for melee and Quadrireme for Ranged. (Moners like Lembos coexists with Bireme and Trireme as melee ships)
B. Trireme for melee and Quadrireme for ranged (a 3d asset project. actually 'Quadrireme as presented in Civ6 has THREE banks with LESS oar than Civ5 Trireme. also graphical representation is very ill presented as the top deck oars aren't manned AT ALL.)
C. Quadrireme for melee and Polyremes (Anything bigger then Quinqueremes) that can fit with catapults
And IF Polyremes is to replace Quadrireme as ranged choice. what should ranges be? One or Two hexes?
EDIT: Is 'Olympias' a best example of Trireme to be referrence for game designing or modding purspose?
2. What are better candidates for 'Melee' ships and 'Ranged' ships in
Medieval era?
Sure Cogs (as well as eastern 'paddle ships , the Qianli Chuan千里船) shown in a chinese Wuxia flicks will be medieval choices. but Dromons and Chelandes as well as less standardized Langskipps including continental derivatives (French Nefs, so often protrayed as 'capable of sails propulsion only and doesn't need oars propulsions') are premier warships of that era. (French Nefs are one such examples)... one issue is that..
2.1 Cogs (as well as bigger Holkes) are still smaller than Mediterranean biggest war galleys of the same era. (Italian CS even evolved Byzantine Dromons further, ultimately created Galea Grossa as dual purpose ships (Freighter and heavy warships, capable to mount catapults and even trebuchets! later switched to big guns)
2.2 'Dromons' are also used by everyone else around Byzantium. referring to similiarly large galleys regardless of origins (Arabians, Italians, or Northern Europeans like French, English, and Scottish).
Are you sure that Cogs can still be Ranged warships? and what about Melee choices? Dromon or what?
2.3 What are 'Naves' actually?
3. Or did the definitions of 'Polyremes' changed by that time and did Galea Grossa also the 'same' Polyremes built with different hulls, (Usually) Lateen sails and dimensions (same lenghts but wide rather than tall) or what?
4. Regarding to missile ships.
4.1 Corvette tend to be smaller than frigates and did have a very limited land attack capabilities. 'Missile Cruiser' in Civ6 is actually Soviet era missile corvette, a very light variants which serves as a better successor to 'Melee ships'. and did see action even as late as 2010s^
And this is around the same size and capability as the late HTMS Sukhothai (Sunk in December 2022) with rather limited inland attacking capabilities compared to something like Burkes, Ticoes, and Chinese Type 055 (The 'Renhai', Chinese, as well as Indian often mistranslated the 055 (and Indian counterparts) as 'Battleship' despite that these have no armor AT ALL). Burkes, Ticoes and the 055 are all have inland long range attacking missiles (or options to do so) but Nancy and Sukhothai didn't.
EDIT2: My 'Trireme' model under construction, it tooks almost a week in modelling which in the same time I have to do research.