Illustrator :: Converting Raster Drawings To Vector?

I have a friend who does drawings on paper that he wants to get scalable.  The high-level path appears to be scan the image and run autotrace in AI.
 
As I look at online articles, some suggest taking the raster into PS to erase the pencil marks and ink the image.  My friend does the inking on the paper before the scan.
 
I have some experimenting to do with autotrace settings, but I can see right away that some of the lines on the image vary in width in both PS and AI.  And, no matter how good his inking is, there is still quite a bit of "noise" along the lines.  His inking also leaves quite a bit of variation in line width.  What he wants is a constant width.
 
My question is: if you want a line to be of constant width and you have a scanned image to work with, which tool (PS, AI) and what technique is best to create the result.
 
One thought is, rather than try to clean up the line in either tool, the better approach might be to draw a new line using the scanned image as a guide.  My concern is that the line won't be smooth if done by hand.