That is certainly an interesting system you use. Absolutely no offense intended, but while certainly detailed, your system doesn't really follow traditional naval classifications based on ship size. Without getting into specialized roles, in general, Destroyers are slightly larger than Frigates, and smaller than Light Cruisers.
If you'll look at the system I use, it is in the "proper" order, if you will, with the exception that, in reality, Dreadnoughts were merely an older, smaller type of Battleship, used around the time of WWI. That said, I chose to lean on the fact that in most popular sci-fi universes and games, the term has come to signify a ship larger than a Battleship.
I did take some artistic license with the use of the term "Leviathan", but I thought it fit well since it is derived from Jewish mythology and means "giant sea monster" (counterpart to Behemoth, the giant land monster). I also felt that having another mythological term on the list lent more relevance to the appearance of the term "Titan", because while Titan, from Greek mythology, is often used in games to classify the largest ships, the term does not have much meaning as a ship classification other than its popularity.
It's my hope that someday Koonschi can find the time to sort out the classifications for NPC ships, so they follow a more appropriate order.
In regards to a ship's material composition, I didn't feel it worth mentioning previously, but since you brought it up and someone may find it useful to have a very simple system, I use the following:
A variant designation of "Mk I-VII" signifies general overall progression and is based on the primary material composition of the hull and armor, followed by the ship's primary material composition for internal systems and weapons potential, where the letters "a-g" are used.
Iron - I/a
Titanium - II/b
Naonite - III/c
Trinium - IV/d
Xanion - V/e
Ogonite - VI/f
Avorion - VII/g
Examples:
Runabout IIc = 1-slot, Titanium Hull/Armor, Naonite Internal Systems and Weapons Potential
Cruiser Mk IVe = 8-slot, Trinium Hull/Armor, Xanion Internal Systems and Weapons Potential
Titan Mk VIg = 15-slot, Ogonite Hull/Armor, Avorion Internal Systems and Weapons Potential