Gauss make good point defense, laying pure point defense ships along with CIWS on individual ships will help you literally just shrug off enemy missiles, and shields will help deal with anything that leaks through, because shields regen for free (well, for fuel).
Particle Beams have a fixed damage output, but they have fixed damage across their entire range. While lasers lose damage at higher range, particle beams deal the same damage, making them able to hit further away for more damage, and giving them a beam-artillery role.
Carronades are reloadable bombs, essentially. High energy drain makes for a slow rate of fire, and their low range combined with damage falloff makes their range very short, but anything that does get within your range will get blasted hard. They seem best mounted on Fast-Attack Craft that are big enough to mount one and quick enough to get in range.
Mesons deal exactly 1 damage at all range, and somewhat short range. Their selling point is that they ignore shields and armor completely, and damage internal modules directly. The trick is, internal modules have only one setting - alive or destroyed. You cannot damage an internal module, only destroy it. Default items have 1-hit-to-kill rating, so any damage will destroy them. Hardened systems might have 5 HTK, so any given shot has a 20% chance to destroy it. Thus it becomes profitable to mount multiple small mesons to give more dice rolls.
While we're at it, Microwave deals double damage to shields and ignores armor, dealing exactly 1 damage to sensor and engine modules, such as engines, thermal sensors, EM sensors, and fire-control. They prove valuable for disabling a ship while leaving it un-damaged, either for marines to move in or for a heavier ship to bring in killer guns, like carronades.
Aaaaand might as well cover all the bases. Lasers deal damage that falls off linearly with their range - the further away the enemy is, the less damage they do. For equal tech investment, particle beams deal more damage at their max range, but lasers deal more damage at closer range.
Additionally, Missiles deal triangular damage to armor, making it difficult to get a one-shot kill unless you're using a very large missile. On the other hand, lasers deal direct penetration, allowing a single laser shot to deal damage to internal components most time. However, missile damage will often overlap with the next shot, letting you beat down the enemy's armor, while laser shots are more likely to hit an un-touched pillar. Thus, if your laser can hit an enemy, it'll hit them. If your laser can't get through all the armor in one hit, then you're going to spend a lot of time shooting at the enemy. Missiles may not penetrate on the first hit, but a second hit is more likely to penetrate.
I want to say that particle beams use the laser damage type, while carronades deal missile triangular damage.