Gauss seems to have a good position as being a point defense weapon for very accurate final fire.
Railguns have the current position of saturation-fire damage, meaning that with proper ranges it can be used as point defense by fighters, or as engagement weapon for FAC.
Mesons are... well. They exist. I guess to cheese anything that wants to rely on any external defensive tech. Good at taking down anything that isn't severely overengineered against it.
Microwaves are good for blinding ships and rendering them helpless before you swoop in with marines.
Particle beams are for getting the highest amount of damage as far out as possible. This doesn't quite work out in practice, though, as the max range for beam weapons is tiny compared to the speed of vessels, and the lasers can be spinally mounted, and use reduced capacitor size, AND can be mounted on a turret, unlike particle beams.

Plasma carronades are effectively placeholders, but could be good for cleanup-crew ships where you just want to erase a helpless ship before it can explore or whatever.

Lasers are good for... just about everything a beam weapon needs to do, really. Point defense, ship killing, alpha strikes, sandpapering, kiting damage... Dang lasers.

Of course, a lot of these don't come up often when there's a missile ship or so lying around, though, if one side's missiles are outright defeated by enemy point defense, then they'll be forced to either retreat, or to engage using beam weapons.