Firefly holds many a weapon in the setting. It ranges from a board with nails to machine guns to lasers and probably items not seen in the show such as nuclear weapons.
Scraps: Pretty much anything you can find that can do some sort of damage would qualify as a scrap weapon.
Alliance Assault Rifle: Standard issue rifles for Alliance troops.
Pistols: Ranging from a revolver to a high tech laser, pistols from just about any age are accepted into the setting.
Stun Gun or Sonic Rifles: Harmless weapons used by the Alliance made to subdue a person. Probably used against rioters or angry individuals.
Cold Light Lantern: A flashlight that can also be used as a weapon. Displayed in the first episode, Serenity, against Shephard Book.
Submachineguns and Assault Rifles: Heavier then a pistol but not the heaviest weapon in the setting.
Rifles: Aim and shoot.
Lasers: Used during the war between Alliance and Browncoats as demonstrated in the first episode, Serenity. They take the form of pistols, SM Gs? and probably on heavier items, such as laser turrets on a ship.
Grenades: Pull the pin and throw.