So I think you would use a kind of 'shop'? Where people can choose and change there skins or backgrounds.
Lets assume that the player needs to have a 100 points in order to unlock and choose the second skin of it's character.
When you want the background to change you have two options I think.
Either use tiled backgrounds, and change the opacity of one another.
Or use a sprite as background, and use the same technique used for swapping animations with the character.
Hope this helps.