In the order: Scout, Light Frigate, Long Range Frigate, Anti-Fighter Frigate, Colonizing Frigate; Carrier, Support Cruiser, Support Cruiser, Heavy Cruiser, Starbase Constructor, Anti-Module vessel, Diplomatic vessel; Bombardment Capital, Battle Capital, EVE Carrier, Battle Capital, Super Carrier.

A word on anti-module component

The Empires of New Eden are similar to the Vasari in that none of them have an anti-module specific ship. Rather, they each have one battleship designed to be built from the Shipyard, coming with substantial anti-module damage.

Amarr

Scout - Executioner. 

Build: 15 seconds, 150 credits, 25 metal, 3 fleet.  Components: 20 EXP, 450 Hull, 200 Shield, 1 HPS, 0.5 SPS, 2.0 Armor.
Weaponry: Beam, Antilight, Overtime, Energy, Beampsi, Front Bank: 19/5.0s, 3000 range, duration 0.2s, Burst 6, Bdelay 0.4. Effects immitated from phase cap colony beam (ffffffff), 3.0 tiling.
Maneuvering: unaltered from TEC scout.
Abilities: Explore, Microwarpdrive, Executioner Propulsion, UnstoppableJumpAmarr, Detect Mines. 100 AM, 0.5AM/s.

*Scout: Executioner. It's their fastest mass produced frigate.
*Light Frigate: Punisher. Will be similar to vasari in that their "Light Frigate" will actually be a pretty heavy frigate.
*Long Range Frigate: Coercer Destroyer; a natural fit.
*Anti-Verylight Frigate: Punisher. The Missile frigates are the best at anti-drone warfare.
*Colony Frigate**: Magnate. It's advanced sensor technology and nice cargo hold will enable colonization. The great thing about this vessel: If you made a few too many, and you need a few extra dedicated combat ships, just do a little expensive upgrading and you have some Gold Magnates!

*Carrier: Arbitrator, naturally.
*Support Cruiser**: Augoror, naturally. If you so desire, they can be converted to Augoror Navy Issue. They sport significantly more ability to take damage than Mallers, and moderate close range damage, but nothing to make it a true tank.
*Support Cruiser: Maller. The Maller is hardly a mainstream combat hull design in EVE Online. It is out paced by the Omen in damage, so it tends to be fitted for supporting and tanking roles. In SoaSe, it will be best suited as a mini-Radiance, with staying power and small radius target forcing. Amarr will be unique in that their most beefy cruiser will be a support cruiser.
*Heavy Cruiser**: Omen. It is mass produced to be fitted for high damage, respectible tank, and that's what HCs do. A cornerstone of the Amarr navy is to convert as many Omen to Omen Navy Issues as possible. Light air support, amazing damage, and amazing tanks cannot be matched.
*Starbase Constructor: Providence.
*Anti-Module**: Armageddon. With less utility ability than Abaddoon and Apocalypse due to slot layout, the Armageddon is mass produced to simply lay down the pain on large targets, but it can still violently tickle smaller ships. By replacing these with Imperial issues, your Planetary assault force will become fearsome.
*Diplomatic: The Sigil is ideal for diplomatic missions. Show them Kor-Azor fervor with this vessel.

Revelation: The Revelation Capital Dreadnought may be restricted to a single target, surging is regenerative and offensive effectiveness. It's planetary bombardment will be unmatched by other Amarrian Capitals.
Abaddon: Built in SoaSe Capital yards, the Abaddon is comparable to SoaSe capital ships; faster than the Revelation, laying strikes from multiple sides, and taking a large amount of punishment.
Archon: Around the Mobility of the Revelation, with similar abilities, but instead comes with some of the more advanced fighters found in EVE.
*Apocalypse**: Although it's range is matched by Revelation, it's maneuverability and ability to deal with a wider variety of threats isn't. The Apocalypse may be slightly weaker than the Abaddon, but may never have to take damage if it can keep proper distance. When endgame is upon you, you have too much cash, and no fronts can be broken, turning your Apocalypse's into something more powerful than the Abaddon while maintaining its range can break the monotony; of course I'm talking about the Apocalypse Imperial Issue.
Aeon: A Super-carrier must colonize, be more powerful than a carrier, but have drawbacks which may or may not be fleet-count, or maneuverability/speed. 

Additional Ships that probably need to make it in

*Prophecy: Harder than a Maller, again sort of like a Mini-Radiance, but with moar buffs. Incredibly fleet inefficient. Don't spam these.
Harbinger: similar to the Prophecy in moar buffs; dissimilar in Harder than a Maller. Maybe it's almost as solid as a Maller, but it can better deal with enemy threats with respectable firepower if it is caught alone. 

Gallente

*Scout: Atron; The speedy Gallente Frigate.
*Light Frigate: Dissimilar to Amarr and Vasari, but similar to Advent and TEC, the Incursus is less beefy than it's anti-fighter family member.
*Long Range Frigate: Catalyst, the destroyer.
*Anti-Verylight Frigate: The Tristan, with both Tracking speed bonus and two missile racks, wins the anti-verylight award.
*Colony Frigate: Imicus find good planet to colonize.

*Carrier**: The Vexor will be a rarity among carrier cruisers in that it will come handy with blasters. Pulling a "fast one" includes but is not limited to turning these into Guardian-Vexors.
*Support Cruiser: This thing (Celestis) makes enemies have a hard time locking targets.
*Support Cruiser**: This thing (Exequror) makes allied hull go back to desirable levels. If you build a couple of these, and would rather see them be hilariously high DPS cruisers, just pay for the very expensive Navy issue lisences!
*Heavy Cruiser: The Thorax is one of the very few heavy cruisers with a drone bay capacity large enough to warrent some kind of inclusion of this feature into SoaSe. It will take on one of the lesser especially made squads of very few drones.
*Starbase Constructor: Obelisk.
Anti-Module: Lacking the tracking of the Megathron, the Hyperion is delegated to anti-module damage components. Violents upon small ships is still allowed.
*Diplomatic: Opus Luxury Yachts are what Gallenteans deploy to show that they care.

Moros: Although lacking in range, this Dreadnought emphasizes one powerful attribute of itself; Single Target damage.
*Megathron**: Perhaps it's the composite/capital (Tracking speed) damage mix that makes the Megathron alluring, or maybe it's the very high base damage it comes to begin with. One thing's for sure, make sure you actually get this thing in range or else you'll have wasted an entire Battleship. Devoting resources to make these Federate issue must come as a last resort. The bonuses are great, but the cost in resources are even greater.
Thanatos: A Carrier that boosts the main source of carrier DPS can be attractive. Just realize that the Thanatos doesn't sport near the best Tank of EVE's capital carriers.
*Dominix**: Did you wish you could play an EVE race and still spam ships similar to the Halcyon, Skiranta, or Sova? Go Gallente. With the Navy Issue Dominix at your disposal, your otherwise fragile carrier battleships can come with highly competitive tanking ability; just make sure the investment is worth it!
Nyx: This is a super carrierr; hear it roar. See it? You read about the Aeon, right? Ok. Take a wild guess what this does. 

Battlecruisers

*Brutix: This ship can deal the pain and regenerate quickly, if in trouble; it has some air support to boot. It will provide invaluable buffing to your fleet. With all this awesome sauce, it's a shame it will cost too much fleet supply to spam.
Myrmidon: The Myrmidon is very similar to the Brutix, but with less direct firepower and more air superiority.

Caldari

*Scout: Obvious choice is obvious. Condor
*Light Frigate:  Merlin. Rock-like medium damage light frigate can be good.
*Long Range Frigate: Cormorant Destroyer. It may resemble a TEC LRF.
*Anti-Verylight Frigate: The Pros know when it's best to built a Kestrel!
*Heron: The Caldari became unmatched in Planet-colonizing when they made the Heron.

*Support Carrier**: The Osprey, a support cruiser, has the largest cruiser-level drone bay of the Caldari fleet. It will be seen more as a Support Cruiser than a Carrier. None the less, it will have more air support than the other cruisers; whether the others are even translated with any air support at all is up for debate. Turning the Osprey into mad missile powerhouse Osprey Navy Issues can have hilarious results.
*Support Cruiser: the Blackbird is a natural choice.
*Heavy Rail Cruiser: The Moa will sport a beefier, more quickly regenerating shield tank, with longer range weapons, but it's DPS is lacking somewhat when compared to other Heavy cruisers.
*Heavy Missile Cruiser**: A Powerful missile boat with range and the ability to lay down the pain, with an average tank, the Caracal. Issuing Caldari Naval Lisences can temporarily render the Moa obsolete.
*Starbase Constructor: Charon can make starbase good.
Anti-Module: Rohk; the Super long range battleship, particularly good at striking large targets, but not so great versus much else.
*Diplomatic: Not to keen on diplomacy, the Caldari thought the badger was the best choice for diplomatic talks. Different from the Sigil in that its interior accommodations are not luxurious, it stays to true Caldari design in function over form. They pack what they need and head out.

Phoenix: This is like the Dreadnought-opposite of a Revelation. The Phoenix provides incredible alpha damage and alpha recovery, but it's DPS and ability to maintain its shield tank are lacking. Being on the wrong side of a few Phoenix class Dreadnoughts can cause you a loss that may prove pivotal, providing Phoenix' isn't the bulk of their actual fleet. If it is, get ready to laugh real hard.
*Raven**: The Raven remains the powerhouse of the Caldari Navy. It's missiles and torpedoes can put out a variety of targets. It's ability to withstand tremendous damage, albiet over a less period of time than it's Amarrian counterparts, make the Raven ideal for massive fights. If you want to see your Ravens make it rain missiles, win the lottery and convert them all to State issues.
Chimera: Do you want to see what happens when you put shield tanking theory on a carrier capital ship? Look no further.
*Scorpion**: There are Cruisers that can lay out more DPS than a scorpion, but the Scorpion has some of the best supporting abilities EVE capitals have to offer. Make a lot of Scorpions and upgrade them quickly. If you want to sacrifice their utility for gnarly defense and Radiance-level tanking through shields, the Scorpion Navy Issue is your friend.
Wyvern: If you honestly need me to explain the Wyvern to you after reading about shields all over Caldari ships, you need a good beating.

Battlecruisers

*Ferox: In true caldari railgun design, the Ferox possess incredibly long range weaponry. Its passive shield tank provides it with incredible staying power to maintain what it's meant to do; buff.
Drake: The Drake is even better than the Ferox at staying in the fight, boosts allies in the same way, and provides a different and more effective form of self defense; missiles. It is all around a better kind of Battlecruiser, but can it maintain that advantage upon higher levels of research?

Minmatar

*Scout: Naturally fast and agile, the Slasher also packs a greater punch than other scouts, for low manning and cost. It's very fragile, however.
*Light Frigate: Just like the Slasher, the Rifter is low on fleet supply cost, quick, inexpensive, and packs a great punch. It is all around an above average light frigate with it's average durability.
*Long Range Frigate: Thrashers are Destroyers.
*Anti-Verylight Friate: The Breacher annihilates small strike craft and drones with ease, and it's speed helps it to quickly catch them.
*Colonizing Frigate: Having the largest cargo bay available to Frigates and the most sophisticated frigate sensor system in the Minmatar fleet makes the Probe ideal for colonization.

*Support Carrier: The Bellicose can both indirectly boost damage and provide a little drone support. Extensive upgrading can lead to long range stasis webifiers; unless the enemy is near the edge of the well, they will not be going anywhere soon.
*Support Cruiser**: The Scythe is fragile, but does a better job than the Bellicose at providing targetting support, and at a longer range. So perhaps with a longer range on its assistance, it doesn't need to be so beefy. Upgrades can bring very long shield transporting as well. If too many of these are made, and you need more firepower in a pinch, convert them into Mini-Typhoons, Scythe Fleet Issues, and have yourself the fastest, most versitle assault force in all of New Eden.
*Heavy Cruiser: The Rupture, of all New Eden Heavy cruisers, combined the straight foward DPS of the Thorax with unmatched speed, and standard heavy cruiser durability.
*Medium Cruiser**: The Stabber is like a quicker, lighter version of a Heavy Cruiser, hence Medium cruiser. Incredibly fast and great damage output will show you the most cost effective quick strikeforce in New Eden. If money isn't an issue, these can easily become hard as a rock and provide a little drone support with the Fleet Issue.
*Starbase Constructor: Huge Fenrirs deploy Matari starbases.
Anti-Module: Maelstroms are designed and fitted to deploy long range Artillery. They can be the best ship in New Eden for immediately (emphasis on immediately) destroying an orbiting body and getting the heck out.
*Diplomatic: The Mammoth is a large industrial ship with all the necessary amenities that make it perfect for this task.

Naglfar: Naglfars are true to Matari design with both missiles and projectiles more eager than anything to tear up the enemy.
*Tempest**: Typical of Minmatar ships, the Tempest fits racks of Autocannons with a couple of Torpedo Launchers. If you upgrade this to the Tribal Issue version, it comes with more strikecraft, incredible DPS, and additional ways to survive in battle.
Nidhoggur: The Nidhoggur is the most supportive yet most fragile of the EVE Carriers.
*Typhoon**: Typhoons are known for being the fastest Battleships in New Eden. They're more than capable carriers, have a diverse arsenal in equal amounts of autocannons and torpedo launchers. If you see the need to purchase Republic Fleet Typhoons, you'll notice a more realiable strikecraft presence, an even quicker Battleship, a moderate increase in damage ouput and considerable increase in survivability.
Hel: Ever wonder what would happen if you made plans for a mothership, had a bad feeling about it, and a lot of things just weren't adding up, but you started building them anyways? This is what happens.

*Cyclone: A well rounded, stable form of damage and rapid response shield boosting are in the basic design of the Cyclone. What puts it at the top of Amarrian target lists, however, is the immense support it provides to the fleet.
Hurricane:  For a ship that's supposed to provide some hefty assistance to the fleet, the Hurricane is only barely more resilient than a heavy cruiser. It's damage output, however, closely resembles that of a battleship. While attacking other battlecruisers, one must be cautious about how long it may take to kill it. The Hurricane poses another threat; will it chew through me first before I can chew through it?

* Most Frigates, Cruisers, Battlecruisers, and Battleships are improved upon Tech II Research completion.
** Many ships can be significantly altered, to the point of losing their standard role, through very expensive irreversible upgrades.