I found that this article "Stacks for everybody" was a fun read (look at the title!), and provided motivation through the example of vector bundles on a space, though it doesn't go that deep: http://www.cgtp.duke.edu/~drm/PCMI2001/fantechi-stacks.pdf

As for things like étale cohomology, the advice I have seen is that it is best to treat things like that as a black box (like the Lefschetz fixed point theorem and the various comparison theorems) and to learn the foundations later since otherwise one could really spend way too long on details and never get a sense of what the point is. I have certainly become a big fan of this style of learning since it can get really boring reading hundreds of pages of technical proofs.