You'll want to take a look at Trapcode 3D Stroke. It's by far the easiest solution for this type of effect that will work inside After Effects.
Depending on how complex you want to get you'll need to separate layers, arrange them in 3D space, animate camera moves and do some color grading. Your project will not be a simple 1 or 2 layer one click solution.
Rick, thanks for the lead! I'll look into it.
Thanks for the link. I'll be sure to read up on it. I know AE is a little bit of a different beast...but I'm excited to learn it!