Illustrator :: How To Trace Hand Drawn Sketch To Single Line Vector Outline

So I am basically a brand new user to ai-cs6 and have been working on a project for a friend. I've drawn up the basic components of the logo she wants, all separate individual pieces. My intention is/was to trace in each piece, and scale, rotate, and clean them up according to how the final piece should look. Where I'm running into trouble is that the sketches are not point perfect, meaning there's some shading in the hand drawn, and the lines are rough in areas. I'm trying to avoid redrawing the pieces because we both are really happy with where they're at.

What I'd like to do with ai-cs6. How to trace very simply a one line vector of the outline of the image. So instead of creating a piece that has stroke straight from the scanned in artwork, I get a single line, with multiple points, that flows the simple shape of the piece. From there it seems it would be pretty simple to just increase the stroke weight and modify the style of line to make it look how we would like. except that since the sketch has some rough line sections ai-cs6 is adding either a lot of detail and making it look pretty rough, or it's missing entire sections and leaving them blank.