My most numerous weapons tend to be small Railguns. Base-tech variants on cheap, slow escorts: commercial engines, barely armoured. These are often my first warships because the only tech they need is fire control speed, and can make up a good part of my fleet by tonnage if not cost.
Respectable 10 or 12cm variants go on fast support ships, for effective point defence that doesn't require excessive fire controls.
My preferred general purpose weapons are 15cm lasers, often the only weapon type on my main attackers. Good at area defence, quite compact, reasonable to get to fire every increment, can match the maximum fire control range. If I lack either speed or weapon range for flawless victories, they aren't bad in a knife fight.
Mesons are employed in point defence PDCs, microwaves in small numbers to suppress stragglers for boarding actions. I don't tend to develop either line much.
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Gauss cannons are the finest point defence weapons with a little tech investment, and can surpass 10cm railguns in everything but range. A good choice, especially if you are also interested in miniaturisation options for fighters and/or CIWS. They don't fit too well into my build preferences initially (beam ships are designed to be either very cheap or very fast, either favours railguns), others swear by them from the get go.
Particle beams are fine if rather inflexible - midsize lasers aren't too bad a substitute. The lance option with its high penetration at range may make the line considerably more attractive.
Large lasers have their uses, especially in situations where strong initial salvos count for more than sustained fire, reduced size further helps in extreme cases. For expected encounters at lower range than usual (jump point defene, nebula actions), large but otherwise low-tech is very economical. However, with defence against missiles as a very high priority, a big main artillery is something I usually put off for a while.
Railguns too large to fire every 5s don't really impress me, 2 small lasers with twice the rate of fire are fine substitutes for lower upfront investment, and again the laser line is more flexible in general.
Carronades struggle to find a niche where they outshine appropriately-built lasers. In this case large ones without much range tech, possibly emulating carronade's benefits with spinal and/or reduced size options. Research costs of the weapons themselves seem excessive, build costs are less extreme but still higher than for similar-performance lasers (of course, we do get 2 free focal size techs).