I completely disagree with Kirby. The mothership is a great first cap. Shield regen keeps your ships alive, especially in the beginning when you're taking neutral planets and need to not waste resources building ships to replace the ones that were destroyed, and at level 3 its a great addition to your battle ball, multiplaying the strength of the guardians ability. It's level 6 ability is actually one of the most powerful as well as one of the least usable. Building your progenitor first and keeping it alive the whole game means that all the caps you build after that are resurrectable. Being able to build a capital ship and boost its level instantly is arguably one of the best abilities in the game, especially in Multiplayer when people will target your caps in the outset of a battle. You just need to know how to use it. THe colonization ability of the progentior has the best bonus in the game, reducing planetary upgrade costs by 20, 40, and 60 percent, which in the beginning of the game, 20 percent cheaper infrastructure, logistics and tactical upgrades means you save a lot of precious resources
Resurrection: First make sure autocast is turned off on this ability. When one of your capital ships is destroyed in the same gravity well as the Progenitor, it's dying level is recorded. Simply cast resurrection on another of your caps, at any time, anywhere, to instantly boost it to the same level as the one that was destroyed. And viola! you can turn a level 1 to a level 10 instantly.
Personally I always build a progenitor first. Then a Halcyon to help manage enemy strikecraft with Telekinitic push, and then the Revelation to protect my ships against powerful lvl 6 enemy cap ship abilities like Missile Barrage and the space eggs Vortex. Plus the Revelation has the Provoke Hysteria ability at lvl 6 making planet bombardment much quicker.