Each wizard model starts with a diffrent set of equipment.

Basic Wizard

Every player has access to this model.
Staff: Basic Staff
Weapon: Blunt Blade

Wizard with Wizard's Hat

Added to the game with the Wizard Hat DLC.
Staff: Staff +1
Weapon: Sharp Blade

Wizard with Patched Robe

Added to the game with the Mea Culpa DLC.
Staff: Bug Staff
Weapon: Broken Sword

GI Wizard

Added to the game with Magicka: Vietnam.
Staff: Patriot Staff
Weapon: M16A1