I want to make overlapping line art in Adobe Illustrator

Right now I am working on a personal project on the side, But I have run into an issue, I know how to give a white outline to everything by having the stroke on while I make a shape, that is fine. However, when there is a part that I want to add detail too, like for an example a hand, and I want add lineart to each individual finger, how do I go  about doing that? Should I make each finger and individual shape? The problem is that if I do that and add an outline, the entire shape including the unneccesary bit gets an outline which is not what I want. There is a picture of result that I want to achieve attached as well as my project with the initial sketch, and how it is currently but I just can't seem to bend Illustrator to make it do what I want. 

Adobe illustrator is a great tool, but the learning curve is quite steep for a novice like me.