BIGGER LIST
Some things we should keep in mind: Dreadnought murders Titan in 1v1. so they can be the same class, just Titan will be bigger. Titan should thus have a ridiculous amount of utility, as suggested before. Titans should be built with the list of capitals.
Let's keep in mind that it is going to be impossible to completely integrate without keeping it balanced (ie: every race will have carrier cruisers, while caldari do not in the game). For simplicity, just use T1 names, and assume T2 is achieved through the research trees. Some classes will not exactly coincide with the class they take in EVE, but 90%+ will. The common classes should be met for balance.
Construction Frigates Amarr Tormentor, Caldari Bantam, Gallente Navitas, Minmatar Burst
Frigates
Scout Vessels Amarr Executioner, Caldari Condor, Gallente Atron, Minmatar Slasher. These are the fastest T1 ships in EVE, as so is this class of ship in SoaSE.
Light Frigates Amarr Crucifier, Caldari Griffin, Gallente Maulus, Minmatar Vigil. These are the 'electronic warfare' frigates in EVE. In SoaSE, Light frigates are early throw-aways, but can eventually turn into 'antimatter warfare' frigates. It makes sense to a degree.
Long Range Assault Frigates Amarr Coercer, Caldari Cormorant, Gallente Catalyst, Minmatar Thrasher. These are the EVE destroyers, all being good for killing other frigates. That's pretty much what the SoaSE assault frigates are good for. These tend to have 1 less non-high slot than the biggest frigate. Their bonus is primarily their range in EVE, anyways.
Alternative Ranged Missile OR Siege Frigates Amarr Inquisitor, Caldari Kestrel, Gallente Tristan, Minmatar Breacher. I know the missiles=LRF in SoaSE mostly, but they are also the anti-frigate frigates... which is what destroyers are in EVE. Instead, they are either a Siege Frigate now, or an alternative long range frigate. I prefer them as an alternative long range frigate, because siege frigates in SoaSE just seem too weird to me.
Heavy Frigates Amarr Punisher, Caldari Merlin, Gallente Incursus, Minmatar Rifter. All very durable because of good frigate tank with frigate radius and frigate speed. They can easily take down fighters, but will have a harder time than a LRAF taking down a Scout Vessel or Light Frigate (but still should win). This is because fighters in EVE are unmanned, and these are less clumsy than LRAFs.
Colony Frigates Amarr Magnate, Caldari Heron, Gallente Imicus, Minmatar Probe. In Eve, these have the highest base cargo capacity, with astrometric abilities. We can translate that into good at colonization (where we go to on the planet!?) and figuring the workings of neutral facilities (How it work!?) The highest base cargo capacity works with colonizing, and the astrometrics works a little with colonizing, but mostly for that neutral facility employment.
Cruisers
Carrier Cruisers Amarr Arbitrator, Caldari Ospray, Gallente Vexor, Minmatar Bellicose. While there is technically only 3 skill levels for the cruisers, there are practically 4 tiers for the cruisers. Vexor would be the most durable cruiser with the most drones, taking up the most fleet. Arbitrator would have the exact same drone amount and capabilities, but with slightly less durability, thus taking slightly less fleet capacity. Bellicose would be roughly the same durability as the Arbitrator, but with less drones, thus taking even less fleet capacity (like the TEC/Vasari carriers). Finally, the Ospray would essentially be like carriers before the SoaSE carrier buff, low fleet cost, low durability, low fighter amount.
Support Cruisers 1 (defensive) Amarr Augoror, Caldari Blackbird, Gallente Exequror, Minmatar Scythe. The Augoror would specialize in armor repair; the blackbird in momentarily disabling abilities/weapons of up to 6 or 8 targets; the Exequror in armor repair; the Scythe in a very gimpy shield/armor repair mix. I know the scythe is something else in EVE. See italicised paragraph at top.
Support Cruisers 2 (offensive) Amarr Omen, Caldari Caracal, Gallente Celestis, Minmatar Stabber. It seems the Stabber, Caracal ad Omen are out of place here, but Vexor was rightly made a carrier and these three are attack ships without a great role in EVE Online. We can make what they do good translate into offensive buffs in SoaSE. This is probably where we're stretching it the most. Omen increases DPS of nearby ships and be upgraded to decrease Antimatter ability usage of one ship. Caracal increases DPS of nearby ships (less than omen) and be upgraded to provide a certain % shield increase within a radius (balances less than omen DPS help). Celestis would be kind of like Blackbird but more so like the disorientation ability of the Advent Star base Transcendia (not as many disables ships though) and be upgraded for a longer duration. Stabber increases DPS of nearby ships (less than omen) and be upgraded to provide a speed boost for nearby allies (balance less than omen DPS help).
Heavy Cruisers Amarr Maller, Caldari Moa, Gallente Thorax, Minmatar Rupture. These will be the most cost effective in among the Heavy/Battle/Heavy Battle Cruisers. Therefore, for the most common multiplayer games. Should someone go to Cruiser level, they will likely spam these as their choice. In the event of stall games, People would likely go to Battle/Heavy Battlecruisers.
Battlecruisers Amarr Prophecy, Caldari Ferox, Gallente Brutix, Minmatar Cyclone. Good cost effectiveness for combat vessels, but less so than Heavy cruisers. They are are good Fleet effectiveness, but not as good as Heavy Battlecruisers.
Heavy Battlecruisers Amarr Harbinger, Caldari Drake, Gallente Myrmidon, Minmatar Hurricane. The cost effectiveness is not bad, but not as good as Battlecruisers and a bit further away from Heavy Cruisers. They, however, are the most Fleet cost effective of the 3.
Capitals
Anti-SubCap Battleships Amarr Armageddon, Caldari Scorpion, Gallente Megathron, Minmatar Typhoon. Although the Carriers and Motherships are anti-sub cap, these are capitals that will also fill this role, as well as other standard capital roles, while being able to get out better than the rest. The Armageddon has decent drones to support kill sub-capitals, generally equips pulse, thus it's damage type being effective against most all classes and has decent battleship speed. The Scoprion can be given massive disorientation or disabling along with an exceptional tank combined with average battleship speed for easy escape, an attribute of this class of capital ship. These qualities also make it great anti-sub capital. Megathron has tracking help in EVE Online, so it's damage type would be greaty increased in effectiveness in SoaSE. It has good speed and proper suppliment of drones, just like the Armageddon, for anti-subcapital behavior. The Typhoon, this is easy... you should know. Best capital ship velocity, maneuverability, good drone capacity. There is a common fit where this thing flings around like an interceptor. It could perhaps act a lot like the Antorak Marauder.
General Battleships Amarr Abaddon, Caldari Raven, Gallente Hyperion, Minmatar Tempest. Hyperion is faster than Megathron, but with less drones, less tracking, and thus less anti-subcapability. It's speed would be primarily used for coming up on other caps and blasting holes in them. The Raven could be given Fair damage with nice long range and a shield tank. The Tempest is just an overall good-speed, "omg there is a tempest next to me" type of ship. The Abaddon blows holes in you like a Hyperion, but has a bit more effective HP!
Other Specializing Battleships Amarr Apocalypse, Caldari Rohk, Gallente Dominix, Minmatar Maelstrom. Apocalypse and Rohk come with ranged damage and good tanks. Dominix is a battleship-agile drone carrier with supporting turrets and a fair tank. The Maelstrom comes with great damage at a moderate range and some great shield regenerative abilities.
Carriers Amarr Archon, Caldari Chimera, Gallente Thanatos, Minmatar Nidhoggur. Let's not gimp the Minmatar just for the lulz. Just keep their carriers about the same. Archon Armor, Chimera Shield, Gallente + fighter DPS, Nidhoggur speed + perhaps slightly better capital turreting & bombing?
Motherships Amarr Aeon, Caldari Wyvern, Gallente Nyx, Minmatar Hel. Same as last. A good way to keep both balanced is cost/fleet cost. Maybe both can colonize with bonuses, just a mothership is more fleet cost effective for combat. To balance this, so the first thing everyone builds isn't a Mothership, is it possible to only allow Mothership building after a carrier is already built? Or it could be tied into the Tech Tree.
Dreadnoughts Amarr Revelation, Caldari Phoenix, Gallente Moros, Minmatar Naglfar. They hit REALLY hard, they tank REALLY hard, they don't do MUCH else. emphasis on much. If we're allowed to pull stuff around with our caps, they would have the most limited ability to do so.
Titans Amarr Avatar, Caldari Leviathan, Gallente Erebus, Minmatar Ragnarok. They hit and tank almost as hard as dreads, and perhaps harder until they siege if the dreads do siege. They should be given the tons of abilities that may be associated with stations. Quick Repair, Shield regeneration, Antimatter restore, Production, Ship hiding inside even? The ability to move ships with them! A lot of stuff here.
Trade Vessels Amarr Bestower, Caldari Badger(mkII), Gallente Iteron(mkV), Minmatar Mammoth.
Refining Ships We can either just give them all Hulks or we can do something else more creative. Two races, Caldari and Gallente, could act just like the advent, exchanging their trade vessels to be refit and operate like Mining Barges. For Amarr and Minmatar, however, we have other industrials for seperate facilities to use. Amarr Sigil, Minmatar Horde.