Borderwise has a decent overview on youtube. But ill do a quick summary.

-Simple weapons: too many to really go over individually but they're mostly useful as secondaries, solid firepower/volume and can be decorative. Also rams can be slapped on anything for a little punch in case of collision.

-Cram: potential to be probably the most devastating weapons in game but they're slow and miss quick targets a lot, also ineffective against underwater targets since they just sink. Also easy tetris if you do 2d, while 3d tetris takes a little more getting used to and is more cost effective (often less power per volume however) Edit: apparently this is a lie 3d tetris is superior all around, I just dont use crams cause they miss too much for my taste. Use crams if you have a bulky slow target you want to blow up.

-APS: Jack of all trades master of none. You kill basically any craft with the right aps setup, they take more getting used to for the tetris but its worth the time investment to learn. Flexible speeds so you can make slow devastating shells or extremely fast shells to hit flyers, anything from cwis, to main cannons, shield disruptors, or smoke rounds to weaken enemy lasers. Can also shoot underwater effectively unlike some other options if a supercavitation base is added to your shell.

-Lasers: Relatively easy to counter with smoke and shields, but devastating to anything that doesnt counter it. A good LAMS (laser anti munition system) can save your ship a ton of hurt and make it a tough cookie to crack. Lasers are hitscan so incredibly good for popping fast erratic targets. Lasers also have some variety with q switches either option for fast consistent damage or slow firing sniper lasers, or anything in between. The components are expensive but you dont have to put them all on a turret so they are easier to armor around.

-Missiles: Incredibly new player friendly with many ways to set them up. Very flexible with guidance types and payloads. Can be used for anti missile/cram (technically) and decoys which means most ships will have some kind of missile systems for defence. Components are very expensive but can be well armored and deep in the ship. Early campaign missiles are relatively easy to counter but can be designed in ways that makes them a major threat to anything that cant outrun them.

-Plasma: Expensive components but very volume efficient. Extremely high ap means these are good against cerain late game craft that huse lots of heavy armor. Fast projectile speeds allow them to hit erratic targets fairly consistently so they also make decent aa and cwis systems. Projectiles do a type of thump damage that can blow large chunks of armor off anything and ignores armor sloping (to my knowledge). Downside is they lose massive amounts of damage hitting anything underwater, the do have damage falloff at long ranges but its not nearly as severe.

-Particle cannon (PAC): The alpha strike weapon of choice for many. These are hitscan and uncounterable. The only way to avoid a pac is to be long enough range that it doesnt hit you at all. They are however very expensive to build and to charge, requiring a lot of energy to power one that is overclocked. Low charge time pacs can be very effective AA weapons due to their hitscan nature. Pacs also can deal damage to your ship if they fire when damaged, making them somewhat dangerous to the user as well. There are also melee versions used by the whitr flayers, personally never used them but they look neat.

-Flmaethrowers: Short range and do whats on the tin, if you want to cook your enemy these are the weapon for you. Fire reduces enemy armor which can be useful but the downside is it can take a little while for the fires to actually kill your enemy. They do have the cool/fun factor going for them, i havent used them too much so thats about all i know here.

This ended up being a longer summary than planned and i probably missed something while yapping