A short description of the different weapons.
Lasers: Long range energy weapon. Damage drops off with range. There is a seperate tech track for the range multiplier and the size of the laser. Final range is the base damage of the laser times the multiplier. Larger weapons are significantly longer ranged. Limited by the fire control as to the actual maximum range obtainable. Lasers can be mounted in turrets for point defence use.
Meson's: Meson's only do one point of damage per shot, but it ignores shields and armor. Same setup as lasers for the range and size, but the actual range on the meson is 1/2 that of the equivilent laser. Meson's can be mounted in turrets for point defence use.
Torpedo: This is a fairly long range energy weapon. All torpedo's have the same range for a given tech. There are two tech tracks. One for the range of the torpedo, and one for the damage value. Thier damage is constant over thier entire range. A laser will hit harder at close range, but be weaker at long range. I often find that large torpedo's are not really usefull now as you can get a better damage over time with smaller faster firing weapons. The maximum range of a torpedo at any given tech tends to be slightly less than the fire control range.
Railguns: Each time a railgun fires it actually gets four independant shots. The range is based on the damage of the weapon times the range multiplier. In general the railgun is cheaper to reasearch but does not have as many rungs in the tech ladder. For a given size a railgun is also much shorter range than a laser. A 10cm laser has a base damage of 3, a 10cm railgun has 4 shots with a base damage of 1. While the total damage is probably higher than the laser, it will have a shorter range and needs to hit multiple times. While it can not be mounted in turrets for point defence, it actully is fairly good in the early part of the game for point defence because of the 4 shots at a time that it gets.
Gauss Cannon: Mainly a point defence weapon. Only does one point of damage but gets multiple shots per turn. There is a seperate tech line for range and number of shots. The maximum is 10 shots every 5 seconds. Unlike all of the previous energy weapons the gauss cannon do not require a power plant or capaciters. It always has a 5 second cycle time. It can be mounted in a turret for point defence use. Also unlike other weapons when in the design window you can choose to make a smaller gauss cannon that loses accuracy. For 100% accuracy you need a 6hs weapons system. A 3hs gauss cannon has it's base accuracy (from fire control) reduced in half. A minimum size gauss cannon only has a 8% chance to hit but is small enough to be mounted in a fighter.
Microwave: The microwave weapons work like lasers, except they only effect electronics. They have a chance to destroy radar, fire controll, electronic warfare systems and passive sensors. There is a line of tech to protect against this but it has to be built into the target systems from the start. Other than that this works the same way a laser does with one exception, it can not be mounted in a turret.
Carronade: Basically a large short range laser. Cheaper to reasearch than the laser but without the range multiplier. it works exactly like the same size laser except it's range multiplier is always a 1. Carronade's can not be mounted in turrets.
Those are all of the current energy weapons. There are also advanced versions for some of them. You have to find them in ruins. They work like the standard versions but with enhanced capability.
Advanced lasers do more damage for the same size and power requirements. This also translates to better range as the base damage is higher.
Torpedo's also do more damage for a given size and power system. Thier range remains the same however.
Railgun's get one additional shot (5 shots instead of 4) per cycle time.
Advanced Meson's. I am not sure if they are working but they should have a better range than standard meson's. Their range is based off of the advanced lasers.
Advanced carronade. Not sure but I think there are advanced versions of the carronade that do more damage same as an advanced laser would.
I have not seen any advanced gauss cannon or microwave systems yet.
Hope this helps
Brian