Capital Build order

For me:

1. Battleship
2. Colonyship
3. Balanced (1 of each, in long games, I'll have multiple fleets consisting of 5 capships and supporting units each.)
4. Abilities. (Because all of the capships have very good uses, not always in one on one, though.)

As Advent I go:

1. Colony ship for quickest expansion.
2. Halcyon carrier once I have a decent sized force of illums, the energy cooldown bonus gives the entire fleet a nice damage bonus.
3. I normally don't have more than a few caps at the end, just a large number of frigates and cruisers, but generally look for the caps that don't fight as much as they support. Something that will help your frigates is very helpful.

As TEC :

1. Colonizer
2. Dreadnaught ( used to be battleship ).
3. Colonizer and 1-to-1 ratio dreadnaughts-battleships.
4. The abilities of the ships are the most valuable. I like Akkan for it's colonizer and Ion bolt. The Marza's and Kol's for the firepower. A Kol railgun is sweet for taking out another caps shields, and a Marza is nice for clumps of ships. If a battle gets dicey I leave the HC's to handle it, save the caps, and meet my re-inforcement wave one or two hops back.

TEC:

1. Akkan (Upped Ion Bolt, it's my anti-mothership ability, great for fleeing caps too)
2. Kol (Need a rock in the fleet, LRMS are fragile)
3. Dreadnaught (Now I can split into two fleets, Akkan and Dreadnaught with some support goes one way, Kol and most of the fleet goes another, the Akkan and Dreadnaught can destory planets and colonize while the Kol and fleet keep the bulk of the enemy occupied)
4. Another Dreadnaught
5. Dunov (Gotta keep the caps alive)
6. Another Dunov
7. Maybe a Sova...it's rare I ever want a seventh...

Vasari

1. Space Egg (Evacuator, nanite bomb ability is the ultimate anti-cap ability)
2. Carrier (The Health cloud is a beaut and I like using it to support Vasari fighters/bombers, they're tough little bastards)
3. Battleship (need a bulwark in the fleet)
4. Seige Cap (need a seige weapon)
5. Maybe the marauder....with the 1.1 buff it'll finally be useful

3-5 are interchangable

Advent (Ahhh....the best ones)

1. Mothership (Need I say more?)
2. Halcyon/Seige
3. Seige/Halcyon (2 and 3 interchange, the seige can freeze enemy caps...very useful against vasari and advent, Halcyon obviously makes the fleet a lot stronger...and it's the anti-fighter cap...really depends on what my opponent made)
4. The Support one...never can remember it's name (Vertigo and Vengeance are beauts)
5. Battleship (I want animosity combined with Vengeance)
6. Another Mothership (Now I can split into two cap fleets, Mother, Halcyon, Seige in one and Mothership, Support, Battleship in another....that's if I need to, I like to keep them all together

7. Another Halcyon
8. Another Support
9+. The rest....if any, are battleships or motherships

I didn't quite follow what you asked for in the guidlines...but

#4. TEC it's the Dunov if you can get it to Level 6 (huge cuts in antimatter costs)
Advent it's the mothership. The thing has malice, shield regen, an ability to save experience on other caps, and it's got the best colonize ability in the game. Best cap bar none.
Vasari it's the Egg. This ship has colonize (worthless special ability), the nanite bomb, the gravity anti-jump warhead, and it's a seige engine by level 6. Probably #2 most valuable ship in the game.

I would say I have seen very few games online where people can use more than 2-3 cap ships (and those that do were very protected and are hermits). Perhaps for very long games it makes sense (think multi-star). I think if you build a lot of caps on a single star map, you are just wasting money. It requires a serious drain of cash to tech up in order to even build a cap (the research alone could buy you 5-6 LRFs)

There is no specific build order: it all depends on the circumstances. In general, most people agree you should get the colonizer first. After that, it's up to you. I usually use Vasari lately, and choose either the carrier or the seige cap as my second. For TEC, I would normally choose the Kol or Marza. For Advent, pick one, they're all good, but either the carrier or battlecruiser are nice compliments to the colonizer.

For the Vasari

1. Colonizer
2. Battleship
3. Carrier
4. Siege ship (3 and 4 can be changed if on a smaller map)
5. Battleship
6. Disable/Repair
7. Carrier
8. Colonizer (if I am doing a split fleet thing, which I usually do. If not, just move everything else up one slot)
9. Battleship
10. Siege ship
11. Disable/Repair
12. Carrier
13. Battleship
14. Carrier
15. Battleship
16. Siege Ship.

I rarely go all the way down the list, but occasionally I do. I sometimes move a few around dependent on the circumstances, but I like to have enough siege, defenses from the Carrier, and enough power from the Battleship. I do not do much with the Disable/Repair for the Vasari, but I like to have at least 1 lvl 6 for Stabilize Phase Space, and if I can get 2 of them, plus their other abilities, it is really useful.

For Vasari

1. Battleship (sue me)
2. The Space Egg of Doom!
3. Carrier
4. 2 Siege (Massed Phase Missles make me happy)


I play Big games so i go with 1 Battle ship and Egg of DOOM! per fleet (thats right i have 4 fleets). In the Current game battle me and my friends are playing i have all 16 cap ships so i have 4 Kortuls, 4 Space Eggs of DOOM!, 3 Carriers, and 5 siege ships.

I am not a big fan of the Marauder and would rather use the space it would take for more Siege Ships ( i like Massing Phase missles.).

Advent:
1: Mothership
2: Radiance
3: Halcyon
4: Radiance
5: Halcyon
6: Radiance
7: Mothership
8: Rapture or the other battlecruiser. (siege)
9: Radiance
10 : Halcyon

Past that would have another mothership and some more battleships. Having several in a fleet leve 6+ makes that anti-fleet ability incredible.

I use my Advent Cap ships as the primary force, with support from Ruthless Crusadors, mixed with from of the enforcers? (the ones with the gravity effect), and a smattering of other frigates.

TEC:
1: Akkan
2: Kol
3: Dunov
4: Sova
5: Kol
6: Dunov
7: Dunov
8: Kol
9: Sova
10: Akkan
11: Sova
12: Kol
13: Dunov

My TEC fleet is more healing based, as I always have a large haul of LRMs, Hoshinkos, and Ceilos in tow. But this keeps the units alive longer, so more EXP for caps.

I don't play Vasari much, but when I do, I build a lot of their carriers. A lot. Mixed with battleships and siege ships.

Well I had forgotten that the owner had not said anything yet..I generally use the advent so here goes:

1Progenator
2Radiance
3Halcyon
4Halcyon-anima tempest, nothing like it...

TEC: Vasari:
Kol Space egg
Akkan Carrier
Sova Battleship
Marza Battleship
Kol 2xSiege
Kol
Sova
Sova
Sova

Well, after a year and numerous builds, things around here have changed...  And as such, I'm brining this back, just to see the difference a year of updates has made...

I am also extending things so that well.. just look at the new template in the first post...

For my personal taste...

TEC

1. Kol

2. Dunov

3. Marza

4. Kol (they are by far the best against multiple enemies of any TEC ship.)

 

Advent

1. Progenator

2. Radiance

3. Halcyon

4. Hard question...

 

Vasari

1. Space Egg

2. Kortul Devastator

3. Something-or-other Desolator

4. The Desolator because of its ability to quickly damage planets and its missile swarm.

vasari

Egg

CArrier

I usually never get past 2 caps just because you should only build your second cap once your egg is lvl 6. the carrier gtives an advantage with strikecraft.

1. marza 2.marza 3.marza 4.badger..err marza

first choice could be everything,just study capship abilities and their effecienty when used with everything else...I once used dunov as first cap to colonize heavely guarded terran - it healed cobalts very nice.

Wow usually I go in this order

1. Siege
2. Battle
3. Support
4. Colony
5. Carrier

Wow ! major difference in a year..

For TEC :

1: Marza

2: Marza

3: Akkan

4: Never really get this far.. But a third Marza in training...

 

After you get two lvl 6 Marzas, you really don't need much else, except maybe a Third... Two really is the blade of your steamroller. Drop in, nuke enemy, raze planet, move on... I use carriers for cover ( fighters/bombers in a 3/1 split ), kodiaks as perimeter defense, hoshis as medics/dis-ablers. Carriers first, with Kodiaks and Hoshi's right behind. Carriers/Kodiaks/Hoshis hold position at jump point. Once most of the SC are gone, add Marzas, If the enemiy was stupid enough to charge my initial group, the Marzas nuke them all. If not, charge with caps and cruisers. Use the Akkan and 5 carriers with all bombers to clean up the system and colonize it, while the battle fleet moves on. Wash, rinse, repeat.

Space Egg of I win

Desolator (I like to get this leveled up so it's ready to really start pounding on early/mid game star bases and get level 6 ability as quick as possible for ultimate SB killer of doom)

Carrier (I get it about when carriers have been researched)

Battleship (Very late in the game I may get this but it doesn't make much of a difference by then, I do it mainly cause it looks cool )

For TEC, I either get Akkan / Marza / Kol or Marza / Akkan / Kol.  Sometimes I'll get a Sova or Dunov, but usually that team of three will be my primary caps throughout the game.

For Advent, Progen / Halcyon / Radiance all the way.  I might swap radiance and halcyon depending on my situation, but otherwise this is pretty straightforward.  If it goes late game and I'm bomber spamming, I bring out a Rapture for concentration.

For Vasari, the Evacuator goes without saying.  If I need siege capabilities and drain planet isn't yet unlocked, I'll get myself a desolator.  Sometimes I'll pick out a Kortul or Skirantra for general support.  If I see a Marza at level 5, I'll get a marauder.  Really I have no plan for capital ships as Vasari, nor do they really need one.  Capital ships are support ships for them.  Get 'em if you need 'em.

I almost always play as Vasari so:

1. Space Egg, for expansion. I usualy build it with 4 scouts and 4 Asailants as my fleet within the first 5 minutes

2. Carrier, for the repair cloud ability. I usualy build it after I get 2 fleet upgrades and level 6 Egg. This is usualy about an hour into the game on large maps and half an hour on small maps

3. Never get this far because I find cap ships to be little more than $3000 targets late game. Sometimes Ill get a Marauder exclusively for the ability that makes your ships faster but I would rather put the money into starbases that can defend my planet and attack enemy planets. Advent are an exception because their cap ships have powerful suport abilitys that greatly benifit the fleet.