A few points:
* You cannot shoot more than once every 5 seconds. If you over-engineer your beam weapons, that is "Give them capacitors capable of delivering more energy than they need to fire once per five seconds", they require more power but do not gain anything. The R6/C4 cannon Sirus posted is perfect - that meson cannon (12cm, I believe) requires 4 energy to fire, and so if you put rank 4 caps in it it fires as fast as possible and wastes no energy. The R6/C10 cannon in the turret, however, has the same power requirement and feeds 10 cap/second (which is quite high tech, btw, mid-game stuff).
* Design your PD turrets to have the same tracking speed as your max beam fire control, that is four times the fire control rating you've researched. Then design a beam fire control with 4* speed (which makes it four times as large and expensive). It is totally not necessary to also make it hit at 4* range, like Sirus has. The two combine to make it sixteen times the base size and cost. And you usually want multiple beam FCs on a dedicated escort. Each one is 800 tons! And for a very small increase in your hit chance at 10,000km, which is where you will be using it.
* Always set your PD fire controls to engage in Final Fire mode and at minimum range - 10kkm. Missiles will almost always travel the entire breadth of your PD beam range in one five-second tick. Final Fire always gets off one snap-shot just before missile impact, Area Defence you don't get that, you fire at visible missiles in the ship's normal turn. So there's no point using them in Area Defence mode, especially since their to-hit chances are terrible the further the target is. And you get a bonus the longer you've tracked an incoming missile for, so waiting is doubly helpful.
* Gauss are the best beam-PD weapon with mesons and lasers roughly tied for second place. The meson and laser tech-lines, however, are more useful for also researching big, offensive beam weapons, while gauss have no range at all. You've got to get to hull-bumping range to use gauss offensively, while decent laser/meson tech will allow you to engage at 200,000km or so. Which remember, is still a really tiny distance in a game where missiles routinely fly 50,000,000km. Offensive beam weapons are only a good idea if your ships are very fast and very well defended.