Anton live-texed notes to Martin's Olsson's course on stacks a few years ago. They are online here. Olsson's notes have been published as:
Algebraic Spaces and Stacks, M. Olsson, AMS Colloquium Publications, volume 62, 2016. ISBN 978-1-4704-2798-6
My general advice is to learn algebraic spaces first. The point is that the new things you need to learn for stacks fall into two categories (which are mostly disjoint): 1) making local, functorial, and non-topological definitions (e.g. what it means for a morphism to be smooth or flat or locally finitely presented) and 2) 2-categorical stuff (e.g. what is a 2-fiber product). You don't need to do things 2-categorically for algebraic spaces, so it makes sense to learn them first. I believe it really clarifies things to learn these separately.
Also, the formal notion of a stack is a generalization of functor. If you are not used to thinking of schemes functorially (e.g. as a functor from rings^op to sets) it will be hard to wrap your head around the notion of a stack. the The intermediate step of learning to think about geometry in terms of functors of points is crucial.
Knutson's book Algebraic Spaces is very good for the EGA-style content, and its introduction will point you to many nice applications of algebraic spaces that are worth learning and will motivate you to learn the EGA-style stuff. Laumon and Moret-Bailly's Champs Algébriques is nice and contains more theorems that just the EGA style stuff.
Its hard to point you any other particular reference without knowing what your goal in learning stacks is.
I would vote for Chevalley's theorem as the most basic fact in algebraic geometry:
The image of a constructible map is constructible.
More down to earth, its most basic case (which, I think, already captures the essential content), is the following: the image of a polynomial map $\mathbb{C}^n \to \mathbb{C}^m$,
$z_1, \dots, z_n \mapsto f_1(\underline{z}), \dots, f_m(\underline{z})$ can always be described by a set of polynomial equations $g_1= \dots = g_k = 0$, combined with a set of polynomial ''unequations'' (*) $h_1 \neq 0, \dots, h_l \neq 0$.
David's post is a special case (if $m > n$, then the image can't be dense, hence $k > 0$). Tarski-Seidenberg is basically a version of Chevalley's theorem in ''semialgebraic real geometry''. More generally, I would argue it is the reason why engineers buy Cox, Little, O'Shea ("Using algebraic geometry"): in the right coordinates, you can parametrize the possible configurations of a robotic arm by polynomials. Then Chevalley says the possible configuration can also be described by equations.
(*) Really it seems that "inequalities" would be the right word her...might be a little late to change terminology though...
Best Answer
Springer printed an Errata supposedly to be included in a study edition of the text to be published in 1977. I purchased the original edition directly from Springer and they mailed me the Errata at a later date. I don't really know what transpired in the intervening years.