Typical of LF (Disciples, Cobalts, Skirmishers). Never really use their special abilities and are often used as meat shields until Heavy Cruisers are brought in.

They are countered very well by LRF and heavy cruisers.  LRF should be the majority of your fleet especially early on.  Rarely is it worth it to have a huge fleet of disciples against the AI.  Sometimes it is worth it online if done well with scout spam to kill LRF.  If its just the AI, then don't worry much about discs and just make illuminators instead.

[_]-Greyfox

lol, well they are technically front line units, weak ones mind you, but front line units. That's why they are put there.

I don't want to even trade shots wtih them.  They're only good behind the lines, sapping antimatter (has a good range to steal).  My cap ship should be in front smiting the heavy cruisers.  Wish there was a way to tell the fleet what ships to have in the front, because the Disciple doesn't cut it.

Just move em behind and use 'hold position'

If the battle moves then move them a little closer  

From the original post I assume you want advice on the early game, so you mean militia heavies.  Capital ships are appropriate to deal with them, though I wouldn't send a single unsupported capital ship into a system with more than one militia heavy cruiser.  I wouldn't use fleets that early in a game, it isn't necessary.

There are two methods of capturing planets at the start of the game.  If you have a colony capital you can take out the siege frigates and leave one or more turrets to deal with the rest.  The advantages are the minimal fleet that is used, allowing any other ships to perform another task, and the speed of capture.  The disadvantage is that it isn't always practical and sometimes you can make a mess of it, also your capital doesn't gain as much experience.  Turrets cost some resources.

If you want to use some light frigates as support, jump your capital ship in first to make it the default target.  When you follow up with the light frigates you should concentrate on any militia long range frigates, which will switch to attacking the light frigates.  Heavies might also switch, you should be careful about attacking grav wells with heavies early in the game unless you can field bombers.  Having your only capital ship badly damaged early in the game is not a good plan.

I'm not sure what you mean about stealing antimatter, as militia ships don't have any, and the technology is expensive to research at such an early stage.  Shield regeneration is not as effective as simply retreating the light frigate that has been targeted as soon as it takes damage.  It should be able to escape and meanwhile the other light frigates are free to fire with no risk of loss. 

That's the Cobalt; this unit doesn't have any abilities until you perform the right research. 

The battleship really only makes sense as an opener for Vasari, since the Kortul has some great abilities.  Beyond this, the Progenitor actually has very good damage output that's similar to a battleship.  The Radiance deals 51.5 damage per second, while the Progenitor deals 48 damage per second (level 1 in both cases).  The difference is nowhere near what you think it is.

If you want firepower, go with the Halcyon-class and spec it with adept drone anima and all bombers.  The carriers are the undisputed kings of damage output as far as capital ship goes.  A level 1 Halcyon, for instance, only has 34 damage per second, but with adept drone anima can sport up to four squads of bombers, which can dish out up to 70 damage per second, dwarfing what the other capital ships are capable of.