In order of range (Which goes up with tech. A high tech weapon can out range a low tech weapon despite lower base range):
Lasers. Lots of range. The higher power ones tend to shoot through several layers of armor, and still have enough energy left to do major internal damage. At least at point blank. Very generic, okay at all ranges, can be turreted. Main interesting thing is that you can reduce their size at the cost of firerate.
Plasma Carronade. Where this belongs in range depends on tech really, because it has no multiplier. Carronades are basically giant lasers. Without the range multiplier, turret mount, armor piercing, or reduced size capability. Junk. Don't let anyone convince you otherwise.
Particle beams. A little less max range than lasers, but they do full damage up to that range. As such, they're pretty good when firing near their max range, poor otherwise.
Meson Cannons. Half laser range. Ignore all passive and active defenses. If you hit with a meson cannon, it does one point of internal damage, period. Quite good at their max range, still decent anywhere in that range. Can be turreted. Expensive.
HPM. Even MORE expensive than meson cannons, and pretty similar. Unlike mesons, they can be blocked by shields. On the plus side, they only do damage to electronics. Even against hardened electronics, these are the fastest way to cripple a ship, bar none. They can't actually kill ships or missiles though.
Railguns. Highest simple DPS, 1/3 laser range, damage is split into four shots. Pretty good at point defense due to all the shots. Goes well on fast parasite ships, where the point defense ability becomes really impressive.
Gauss Cannons. Inferior railguns that can be turreted. They are somewhat different, but that's what you need to know. Good for anti-missile turrets, mostly useless for anything else.
Power generally goes up as range goes down, most weapons are (relatively) best at the edge of their range. Enough lasers will beat anything of the same tech level. Or just one if you're faster and they're out of missiles.