I know you can easily make a cake/gumpaste figurine spin, but my concern is how do you make a figurine move in a straight path? Does anyone have a suggestion?

It depends on what type of straight line. Do you it to move in a straight line back and forth or up and down? Do you have room under the cake for the motor? I assume back and forth....when I get home I'll try to mock something up and post a pic for you.

Sorry for the extreme sloppiness of the mockup, I grabbed some scraps and clamped it together. This is the basic idea. As the motor turns it moves your slider back and forth. The slider is sandwiched (loosely) so it can only go in the one direction. Attach a wire or dowel and put your figure on it. All of this would be under the cake or inside some compartment inside the cake (foam core, styrofoam etc).
(note: the steps in the white slider are only there because this was scrap, it should be much simpler than this, easy rectangle would be good)

Video:
http://www.willyliliana.com/Cakes/Move.mp4