The most basic weapon type is the pulse laser, which shoots for short intervals. The 1MW version is very weak but the 5MW is useable. The 30MW mining laser is quite powerful, but has rather a long cool down. This makes it hard to hit small fast moving ships.
Most players will want to equip themselves with a beam laser. They do plenty of damage to large ships while making it easier to hit small fighters. Resist the urge to pack the biggest laser you can - any beam laser will kill things at reasonable speed. First consider the need to have a few shields, a decent hyperdrive, vital equipment and maybe some trading space (see also Combat Equipment).
More powerful lasers overheat quickly. The 1MW beam laser does not overheat easily. The 4MW, 20MW and 100MW versions should be used with a laser cooling booster. The 100MW version overheats a little too quickly and is not recommmended, since the 20MW version is deadly enough and overheats less.
No matter how many shields you have, the enemy can kill you pretty quickly with high power lasers. They have a weakness though. If you can dodge them for a few seconds any beam lasers from 4MW upwards will overheat and become far less dangerous.
Effectively just more powerful beam lasers but with one key difference - they take a long time to overheat and for practical purposes they don't. The question is whether you want to sacrifice 500 tonnes for a small plasma accelerator when a 20MW beam laser can kill any normal target very quickly with just 75 tonnes.
The large plasma accelerator is the ultimate weapon that pilots aspire to owning. That is, until they get one and realize that the small plasma accelerator is just as effective and leaves 400 tonnes of space free for shields etc. There isn't really any room for improvement over the small plasma accelerator.
Missiles are not a good weapon in most cases. With the cargo space that two missiles take up, a 1MW pulse laser could be upgraded to 5MW, a 5MW could be upgraded to the 1MW beam, or it might let you squeeze in an extra shield. It is also impossible to carry enough missiles to kill the dozen or so ships that sometimes attack. The best use for missiles is against small, nimble fighters that are difficult to hit with a laser.