I have just started experimenting with 3D figures and hoped to get some advice. First what medium is best: fondant, gumpaste, candy clay, etc.? Second, I have an idea to do 3D stick figures of a friend's family for a birthday cake. What types of materials are best for providing support/stability?
Any help would be greatly appreciated!

I have never worked with gumpaste or candy clay. But the fondant works well if you take your time and let it dry.

you can use gumpaste but i use rolled buttercream. you can use play dough books for ideas or instructions. follow the instructions but use rolled buttercream or gumpaste for figures. if the dough is too moist just add a little gum tex and confectioners sugar to give it more body and dry faster. form your pieces and let dry a little bit then glue together with clear piping gel. check out my figures used on my cakes. they are all made with rolled buttercream glued with clear piping gel. great fun. good luck and email or post to my address if you have problems. practice makes perfect.

you can use toothpicks or straws for support in your figures. let pieces dry a little bit then coat toothpick or straw with clear piping gel. toothpick stick inside formed pieces after drying a little bit, build and form pieces around straw while forming then let dry a little bit before standing them up. works on my 3d figures. have fun!

If you look on youtube for any of Aine2's video she has lots that explain how to make figures from gumpaste/fondant. She explains every step and is easy to follow. That is how I learned.