I did some numeric analysis, and came to the following conclusions:
1) mounting different categories of weapons NEVER makes sense, since you're giving the defender's defenses two chances to reduce damage.
2) If you've got two different defensive techs and you're fighting an enemy with mixed weaponry against both types, you're better off mixing defenses on the ship. The same goes for a situation where the one ship may be fighting two different enemies. Note: This can be avoided if you manage your ships very carefully and always have the correct counter on hand. Not something I'm good at.
3) Offense only ships may sound like a good idea (they are at first), but if you have any tech lead, you're wasting ships by not placing defenses on your ships. Because defenses tend to be more compact than weapons once you get out of the first or early second tier, a ship that you could put 12 Attack no defense could probably be 8 Attack, 6 or 8 Defense, which as long as the defense matches the other's attack, will shred a 12 Attack ship.
4) Mixing weapon categories within a fleet can be loads of fun, as the enemy has little or nothing to adapt to

I've had a few games last long enough that I had all the weapon and defense techs, and my favorite fleets consisted of three classes of ships, all with the same speed/range, approximately equal amounts of all three types of defenses, and one type of weapon. That way, in a three ship fleet, I'd have one big attack of each of the three types of attacks, and usually the victim ships would have defenses against two at most.
And, from my play experience, if you think it's best to focus on a single defense for research purposes, you're going to get slaughtered in higher level games that aren't short. In the post-1.0 testing I did , if the war wasn't a short one, by the end of it, the enemy had adapted his ships to my prefered weapons and defenses at least once, and in one case, twice. This wasn't even on Intelligent, it was on Bright, as I'm only winning about a quarter of my Bright x 9 opponents/Gigantic galaxy games.
The later in the game, the more true this is. You might not think that having the wrong type of defense is a big deal when it comes down to a defense of 4 vs 2, but when it's 60 vs 8, you'll notice.
I think I'm going to have to drop back down to Normal difficulty. It was too easy in the beta, but the Gamma and post-production AI is so much better it's scary.