Your safest bet for all situations is probably a Halcyon.  Based on your starting position, if it looks like rapid colonization and econ are most important, make a Progen.  You'll probably build a Halcyon later once you start to fleet up.  If it looks like you will be fighting very soon (front line on a crowded map) build a Halcyon.  You will probably build a Progen later so Shield Restore can maximize fleet survivability.

Radiance and Revelation are situationally good ships if you have to fight someone toe to toe, but not that great if you are fighting against hit and run or kiting tactics.

95% of the time you want the Halcyon for your starter cap.

Idk.... the Dunov and the Kol are kinda late-ish game caps. Iv heard of dunov's being used well early on but I haven't seen it personally and the Kol is only useful past lvl 6. The Marza, Sova and Akkan are different stories.

The problem with the Kol is getting it to level six without it being shredded beforehand by focus-fire LRMs. Lower level Kols will very rapidly run out of antimatter and will become an overly expensive brick with poor DPS (on a cost for damage basis).

Capital SC squadrons are also built for free, and can be constantly rebuilt (probably faster than Flak Burst can kill them).

I say progen just for the fact or very rapid expansion ( i usually build 4 scouts and 4 disc to go with it) and for the fact that given you are getting cheaper planet upgrades you can get 2nd cap which for me is halcyon for free or at least as great discount. 

I think that progen is best if you do it as first cap or not build it at all but if you go against tec or another advent lvl5 progen is hard to kill. If u have 2 guy will loose half of the fleet before he focus fire kills 1. But reality is that you do need to get air supremacy if not u are most likely to die so u do need to build halcyon. 

Personally, I always go for the Progen first. It has the easily acknowledged best early-econ boosting ability in the game (low cost planet upgrades are an amazing advantage) that should give you enough of an advantage to counter any rushes the opponent makes. Enough to at least get a second cap ship out (Halcyon is my favourite though I have used Radiance to counter a capship heavy fleet before). As well as that, the idea for the Progen, in my mind, is to expand as quickly as possible toward the enemy, denying him the chance to rush you since you would effectively be rushing him, while not completely forsaking econ build up through the cheap planet upgrades.

Carrier ships and LRF are the mainstay of the Advent at this point, and a medium sized force of LF to counter the flak that should pop up soon is a good idea (keeping them out of range of combat for that period of time is a good plan too.

Of course there is a lot to be said for the Halcyon as a first cap build, what with AEA and such, but I don't believe that forsaking Advent's only econ advantage at the start of the game is a good idea in any scenario (perhaps not for 1v1 small maps though, since you generally don't have time to expand far in those games).

I like the halcyon first as it makes wiping out militias so darn easy and it gets it the xp it needs to head up an invasion army.

If you start /w progen, how fast do you guys get your 2nd capital up?

The Radiance will be an interesting ship again with the beta patch. For one animosity will actually work for the most part as it is reapplied every second for the duration of the ability. This means a new order won't override the animosity anymore.

This may make a Rapture/Radiance combo somewhat interesting in multi-player with a Vengence/Animosity combo.

It's damage dealing capabilities is still pretty meh by itself. I'd like to see DrainAntiMatterAndDoDamage split into seperate overTimeActions. As it stands now, this ability does no damage if the target ship has no antimatter reserves.

Why? I'm don't see why this would be bad or throw balance off. It would actually help to balance Adent capital ship selections with the other races. The interesting builds in soase should be around capital ships IMO.

In my opinion Advent is lacking in two key areas for capital ships compared to the other races.

1. A damage dealing capital ship (non-carrier class), which I'm proposing tweaking an existing ability on the Radiance. TEC get the improved Kol and solid Marza and Vasari get the Kortul, Jarrasul and Desolator and you could probably count the Maurader's phase out hull too. All of these ships have direct damage dealing abilities that work 100% of the time.
2. The second is a viable early game siege capital ship. I doubt this will ever happen, but trying to get a Revelation to level 6 is pretty iffy even mid-late game as you have to field carrier caps to even survive to this point which spreads the experience pretty thin. It would be nice if Advent had a goto siege capital ship like the Marza and Desolator for the other races.

Not to mention one of the best siege animations in the game. Would be nice to see it more often in PvP games.

The devs will never move/remove any abilities. It would obsolete all the paperback stuff that comes with the game.

Ok... manual check complete.

It lists Reverie/Guidance/Clairvoyance/Provoke Hysteria.

So make Guidance the ultimate and add AM recharge to the ability.

Make Provoke Hysteria a 1/3/5 ability.

You don't even have to move them or rename them and the manual doesn't say one word about what they do so we're golden