By default there is only one outfit available which is the Tophat. You can unlock various other outfits by completing objectives, defeating the end-boss, or signing up to the Orangepixel newsletter. The various outfits change the starting skills of your character.
This is your standard outfit. It has no extra skills or powers, and is the standard way to play the game.
The knight is a stronger character and is unlocked by completing 5 objectives. The knight gives you +4 attack and +2 agility and +2 craft.
The wizard hat comes with powerful magic powers, and is unlocked by completing 10 objectives. The wizard gives you +4 magic, +1 luck +3 Alchemy and +1 craft.
The voodoo mask is unlocked with a secret code, to gain this code you need to subscribe to the Orangepixel newsletter, and it will then be auto-send to your mailbox within a few days of subscribing. The voodoo mask gives you +2 attack, +2 magic, +1 luck and +2 agility. As a bonus it gives a special skill: Fear.
Skelly is unlocked by defeating the boss. It will give you +3 attack, +2 magic, +4 luck +3 craft and +4 alchemy.