Just a reply for those who say fighters are destroyed too easily... the most effective design I have takes 2 shots from a PDC before having one destroyed. Large Fighter, 1xCockpit,1xLifeSupport,3xEngines,1xAfterburners,1 xSmallShield,1xCombatSensors,1xECM,1xTimeDistortio nBurst,3xElectricDischarge. The major thing with this design is you need both Temporal and Organic technology, although I'm sure a modified design that is nearly as effective could be made with one or the other tech, or with just standard tech.
Against shields, one fighter will do a max of 120kT damage, and against armor a max of 75kT. Multiplied over a group of 10 or 20, they become quite leathal, and if you use decoy fighters (same as above, only take out weapons and replace with shields) to draw away PDC and weapons fire, they can take out quite a few ships. On top of warps, I've had a group of 11 (one turn's build with Temporal yard on a 4B pop planet) take out AI cruisers, since both ships start very close, the enemy has no chance to defend.
I believe in my AI probing game I destroyed 250kT in ships before it became too much of a hassle to ferry fighters to the front lines and my capital ship design was doing so well (5mT destroyed thus far I believe, 112 constructed, 6 lost).
Now, for the "exotic" weapons as you call them: I believe they are some of the most underrated weapons in the game. Granted, it's not something you want to fill every ship with, but if you have one of these on each of your main attack ships, it can be very useful. Against the AI, I would normally go for big guns, one Ionic Disperser, one Tachyon Disruption Cannon, one or two PDC. The PDC take care of most missiles and fighters, a barrage from the TDC and a shot from the ID (I'll be abbreviating from now on
will disable ships so you can mop them up later and focus more guns on the others. ID are also useful for dropping into a range of six and disabling the movement on several ships, then moving out of direct-fire weapons range (which is 8). That way, a relatively small fleet can effectively disable, target, and destroy large fleets (don't try in strategic mode, the AI doesn't use 'em very effectively).
I think I caught everything I wanted to reply to...