Well, first off, you'll be disappointed--there is no set list of weapons.
The reason? Well, lets take an example. I might think a heavy rail cannon is an extremely powerful weapon that can cause immense damage to anything it hits, while you might think of a heavy rail cannon as being a weapon that can cause some damage, but you think that lasers cause FAR more damage. You see the problem? What I think a weapon might be is different from what you think a weapon might be.
Generally, the weapons in Brigade are fairly normal--most people design vessels of the sizes in Brigade, and their weapons are fairly standard. I tend to design far heavier weapons, just because of my luck at rolling dice--if Im able to penetrate the enemy shields I know the ship will hurt...:D
Heres a general feeling of what I feel weapons should be like. Please disregard them if you wish--as Dan says, its a free game, and you can tinker around with it as much as you want...:)
Rail Cannon: Long range, fair accuracy, Extra Hull Damage, Re-Rolls PEN.
Plasma Cannon: Shorter range, accuracy better/worse, Range-Based DMG, Extra Hull Damage
Laser: Long range, good accuracy, Re-Rolls TH
And so on and so forth.