Use Spriter to do the animation part. You can use either Photoshop/Gimpshop or Illustrator/Inkscape to do the character design.
Create a stickfigure as vector graphics or bitmap, and export the different parts as png images. (you only need one png file for each shape as long as the pivot point should be placed identically)
Make it dance by creating it in Spriter, and adding bones, and adjusting key-frames. (you should do three animations where the stick figure does different stuff)
Make your own character in vector graphics or bitmap. Remember to have different small images that together comprises your character.
Export the images of your character to png, remember to only get your images, and not background or a lot of unwanted transparent space around the parts.
Use Spriter to animate your character.