How do I unlock new paint jobs and gear for MouseBot?

You can use the Prize Machine to win random paint jobs and gear, or you can purchase them individually using Power Tokens.

Nagivate to the inventory screen by clicking on the hat/paintbrush button on the main menu, or on the rewards screen at the end of the maze.  Here, you can freely browse and buy new stuff, or you can use the Prize machine to win a random prize.

To play the Prize Machine, hit the button on top with the present.  If you have enough cheese, you'll activate the machine which will reward you a random prize.  You can apply the prize to MouseBot or cancel out -- either way you'll keep the unlocked prize in your inventory.