Going Commando

it works with almost all caps, the only problem is it takes much longer. usually to colonize faster you build ships to accompany your cap ship.

but for Akkan and progen what you can do, is just get them to kill the lrms and the planet bombing ships, build a turret and send you cap to the next planet. it allows you to colonize really quickly with only your cap.

While I haven't watched the replay yet, I've done similar things in the past myself.  The thing is that the Marza has relatively high DPS for a starting capital ship and can in fact clear a world of militia (provided there aren't too many and the enemy isn't too close).  This will leave it damaged afterwards, and so researching repair bays is pretty much mandatory.  In fact, if you destroy the siege frigates first you can sneak in a colony frigate, colonize the planet, and build a repair bay while you're still fighting the militia.

A strategy like this works only against militia, however.  The only militia units that deal more than marginal damage to a capital ship are LRM's and Kodiaks.  Simply put, it doesn't have enough of these to threaten a capital ship, which is why the capital ship on its own can bring down a neutral world.  A player, on the other hand, is going to build lots of LRF, and they're going to be lead by a capital ship of his own. 

There is no question that a Marza that can fall back to a repair bay is a powerful attacker and defender, but against a well designed early game fleet it will die.  I suspect in this case that Cykur may have started in a position where his enemies were too far away to rush, or he would already have LRF by the time their forces arrived.

This doesn't work with a Progen (at least not well) because it's a low DPS capital ship and it takes positively ages to get through even a small militia.  It will work with the Akkan.  I don't know why you'd try it with the Sova or Halcyon.  The Sova is probably better off embargo rushing and using the extra cash to build a strong early game fleet.  The Halcyon just is such a trade-off from the progen that I can't see it being worthwhile.  In fact, you'll definitely save more from the Progen's colonize ability than the Halcyon could theoretically save you on disciples.  However, the Kol and the Space Egg are both great at this.

A Mazra is the strongest neutral planet cleaner you can get. You can send it in on it's own and for the most part it can be left alone while you focus on other needs. Terran and Desert planets will need caution and maybe 1 or 2 trips to a repair bay before they can be cleared. Sova is very good if you pick Missile Battery as it's ability and suprisingly is only second to Mazra in it's ability to clear neutrals. Akkan is also stronger than it first may apear but you may have to move it into the middle of the enemy so both sides of the ship are shooting at targets. Halcyon is not particulary strong and is much slower at clearing neutrals but it does leave the fight with more health points but the Radiance is best for Advent in clearing neutrals.

I get colony ships anyway for nuetrals, and really early in the game, I find the halycon's increase in dps to the lrm's outdoes the progen shield restore.  Progen usually is my 2nd cap rolling out with guardians and carriers.

That presumes that there are neutrals nearby the planet in question that you are colonizing.  If this is not the case (which is most likely) you will need two colony frigates, whereas someone with a progen needs only one.  In practice, a colony frigate doesn't have the anti-matter regen rate to be colonizing, capturing neutrals, and phase jumping early on.   Besides that point, you're going to save a bundle with the progen's built-in 20% planet upgrade discount.  If there are terran or desert planets, then the advantage of the progen just becomes absolutely insane.

Even the claim that energy amplification is a better deal that the progen is dubious.  Level 1 energy amplification gives you a 7.5% damage boost to your fleet.  For every 13 illuminators you have, it's as if you have 1 extra illuminator dealing damage.  So, if you have a 26 illuminator fleet, energy amplification makes it as if you had 28 illuminators attacking.  If my progen saves me enough money for two extra illuminators (it will probably save more than that...) then I have just as much damage as you, plus the additional hit points of my two illuminators, and shield regeneration.

So, I'd argue the mothership is better than the halcyon (as a first cap) even without shield regeneration.  Its colonize ability is just that good.

Halycon reduces the weapon cooldown, that is more effective than a plain damage-percentage increase. E.g. 50% cooldown reduction equals 100% damage increase. The exact dps formula would damage per shot / [(shots per second) * fire-ratio-constant], which would normally be 1, for unmodied. If you reduce that constant by 10% to 0.9 that'd increase the overall damage by it's reciprocal 10/9=1.11111111111, which might be pretty close to 10%, but the margin gets bigger with increasing cooldown reduction.

Bottomline is: halycon is definitely worth it's money, but I wouldn't advise it as first cap. Either Progenitor for colonization/fleet-durability or Radiance to counter nasty AM abilities like Nano-Disassember and MB.

I don't always do this...sometimes I make a handful of cobalts because expansion goes much faster with backup.  It kind of depends on my overall strategy, and in this game I decided to rush LRM.  I knew the Marza would do reasonable well until backup could arrive.

All of the battleships, colony capitals, and several of the other caps can clear most worlds solo, even if it is time consuming.  Some of the lower DPS caps probably shouldn't do it, not because they can't, but because it is a pretty big waste of time when they are unsupported.  Imagine clearing with a Marauder?  gah.   Marza and Vulkoras do quite well because of their powerful foward arc and their initial damage abilities.