Wands and staves allow you to increase the MP pool of your character. The limitation is that they can only use those additional MP points to cast the spell stored in them.
Broadly speaking, a similar quality staff will have 1.5 times the MP pool of its wand counterpart. Enchantment can be used to increase the MP pool of a wand or staff.
A blank wand or staff can have any spell the caster knows added to it. Once this is done, however, it becomes a wand or staff of that spell and can only cast that spell. Certain higher quality wands or staves can have more than one spell effect added to them. In these cases, both spells must be cast simultaneously at the cost of 1.5x the average MP cost of the two spells.
Light weapons are weapons like daggers or shivs. Lighter weapons than normal one handed weapons. Focussed on precision to deal damage instead of the weight of the weapon itself.
One handed weapons are weapons like broadswords, battle axes and maces. They are heavy weapons and deal significant damage but are light enough to use in one hand, keeping the other free for a shield or another weapon.
Two handed weapons are weapons like claymores, greataxes and warhammers. They deal devastating damage but require both hands to wield them.
Machine weapons are weapons like crossbows and guns. The damage they deal is fixed and the skill of the user only determines where the attack will land.
Archery weapons are weapons like a bow and arrow. A device is used to fire a projectile, but all of the power for this still comes from the weapon's wielder.
Thrown weapons are anything that is thrown. Typically, this would be a weapon designed specifically for throwing, like a throwing knife, but anything that can be thrown can be considered a thrown weapon.
Improvised weapons overlap to an extent with thrown weapons. A weapon counts as improvised when used for melee and as a thrown weapon when it is thrown. Any random object that you could hit something with could be used as an improvised weapon. The base damage is to the DM's discretion.
You can use your improvised weapon skill in place of any other melee weapon type at a -2 penalty.