Ok. First you need to evaluate where you are on the map.
If you are in the economy spot, the Progenitor makes the most sense, the colonization bonuses make logistic slots easier to obtain. If you are in the economy spot, there is rarely any need for another capital ship though, unless you are forced to fleet, if this is the case, see below.
If you are fighting, the Halcyon really should be your unanimous choice capital ships.
Each of the three abilities the halcyon offers are extremely helpful, and i would prioritize them in this order
1. Adept Drone Anima (Extra Squadrons)
2. Amplify Energy Aura (Reduces cooldown on weapons, essentially increasing dps on each ship, which is awesome.)
3. Telekinetic push (Great for keeping bombers off a sb, or just from harassing your fleet.)
After my first Halcyon i usually go one of two ways (another fork in the road)
A. Fighting still intense
Another Halcyon really is quite practical in these situations, increased air superiority is crucial and forces the enemy to contemplate flak, in which case you can produce even more illuminators and crush him.
B. You beat the guy you were fighting, and now you need to continue on another guy.
Get the Revelation the Revelation has a couple really great abilities for this situation.
Faster bombing is great, as you want to be done as soon as you can with the guy you are fighting, and onto the next guy.
Also, the Revelation has the Clairvoyance ability which allows you to spy on other planets and place a remote sensor there for an extended period of time, so you can have a heads up on when your enemy is coming.
C. You got your guy, and now its time to ease off, kill his planets and establish an economy.
The Progenitor is the best choice, as the colonization bonuses will come in handy when setting up an economy.