Fist: For those who prefer bare-knuckled brawling.
Club: A long, oblong piece of wood perfect for beating zombies into submission.
Knife: Excellent for spreading butter on your toast; less so for fighting the undead.

Normal Knife: An ordinary knife with a decorated handle. Intended for use by ladies for protection. Dirk: A simple double-edged blade; more decorative than functional.

Saber: A light sword for poking holes in your enemies.
Two-Handed Sword: A heavy sword for gashing dark creatures.
Axe: Chopping wood is no different from chopping zombie limbs.
Spear: Long-distance poking power.
Bowgun: Because why use bullets when you can use arrows!
Single Action Pistol: A girl's best friend in a dark alley.

SA Pistol: First issued in 1874, this single-action revolver saw much use in the American West.

Rifle: Perfect for hunting mutant rats.
Shotgun: Eat lead, you damned zombie!

Each different kind of weapon comes in multiple flavors, and many have significant magic/status attributes, which are designated by an adjective affixed to the weapon name, such "Mystic" (which drains MP from opponent and feeds it to you).

Once you used a weapon long enough, it will break. There's nothing you can do to prevent this. However, whatever level you gained with that weapon will also carry over to any other same-type weapons you use.