Contrary to marketing-driven misconception, the primary purpose of programs like Illustrator is not "automatic conversion" of raster images to vector-based paths (i.e.; autotracing).
Bezier drawing programs are primarily all about drawing accurate vector (math formula-based) paths deliberately. That necessarily means drawing them manually and knowingly.
In other words, for your stated purpose, you should not be doing this by starting with autotracing at all. You shoud be using the various drawing tools to methodically construct the artwork paths manually. Yes, the quality of the results is dependent upon proficiency. That's just the way it is in vector-based drawing, just as it is in just about anything.
Quality (including accuracy and economy) in vector-based drawing does not come from merely owning software, just as quality work on your car does not come from merely owning a wrench. In the vast majority of cases, using autotracing is just like a shadetree "mechanic" using a pair of pliers to turn a hex bolt. Both should make you cringe. Yeah, the pliers-wielding buffoon (and no, I'm not calling you a buffoon) may get the bolt to turn; and someone who never looks under the hood may never know the difference. But would you knowingly take your car back to such a "mechanic"?
Forget autotracing. It's crap. It has no shape-recognition intelligence. In Illustrator, it doesn't even know an actual circle from any other "sort of roundish" curve. The same can be said for features like Smooth, Roughen, etc. No, they are not utterly useless. But they should be used with knowing discretion.
Buckle down and learn to draw paths accurately, efficiently, and economically. It's not rocket science, but there is no instant substitute. The kind of task you are describing is the very kind of work which serves best as learning exercises.
JET offers very helpful guidance. Though learning to draw precise paths can be time consuming, remember that practice makes perfect.
I came across a tutorial about moving from a sketch to a finished vector illustration that outlines how to create shapes with the pen tool and using brushes. Find it here.
I have also found the Width Tool to be extremely helpful in creating line variation. Below is a great video about how to use it.
Good luck in your drawing endeavors!