I would like this thread to contain possibly useful information about books and approaches on studying scheme theory for the first time. I'm truly sorry if one finds it inapproprite for this site, but from the experience I had with math.stackexchange I think that I've seen more "vague" threads.
Nowadays we have a massive number of introductions to modern algebraic geometry (scheme-theoretic, not complex, though in my humble opinion "algebraic geometry" is a bad name for the study of complex manifolds, "complex analytic geometry" describes the subject better) developed by Grothendieck and his school. I'll list the ones I know:
Ravi Vakil - "Foundations of Algebraic Geometry" (free on his website, very conversational and leaves a lot of stuff to exercises)
Robin Hartshorne - "Algebraic Geometry" (the classic, but studies only Noetherian schemes and possibly too formal for first times)
Ulrich Goertz and Torsten Wedhorn - "Algebraic Geometry: Part I: Schemes. With examples and exercises" (600 pages of scheme theory, but no cohomology which is reserved to yet unpublished second volume)
Joe Harris and David Eisenbud - "Geometry of Schemes" (introductory text on schemes, not a complete course on algebraic geometry, rather a text which tries to develop reader's intuition for studying schemes)
Kenji Ueno - "Algebraic Geometry 1/2/3" (was published in 1999 by AMS, but apparently not well known by western community as well as by me)
David Mumford and Tadao Oda - "Algebraic Geometry II" (expanded and updated version of Mumford's famous "Red book", seems neat and friendly)
Liu Qing - "Algebraic Geometry and Arithmetic Curves" (arithmetically flavoured text)
Alexander Grothendieck and Jean Dieudonne - "Elements of Algebraic Geometry" (the first "book" on algebraic geometry, very abstract and complete, 1800 pages-long, but exists only in French and possibly contains more than an beginner needs to know. But, maybe, even if all 1800 pages are not needed to learn scheme theory, they can be helpful to master it)
The (not algebraic, mind you) variety of books is definitely a good thing. But it can be daunting for a novice to choose which one to use? For example,
If one's inclinations lies in category theory and homological algebra/algebraic topology, which books emphasizes the "categorical" and "homological" modern approach? Introducing as much homological algebra as can be useful for the basics of scheme theory? (EGA is a possible candidate, people say it's very abstract)
If one likes to think about mathematical objects from a "geometric" point of view, which book emphasized geometric intuition and connections with other areas of geometry more? (Eisenbud-Harris could be a candidate along with some course on classical algebraic geometry, as the sole purpose of the former is to help a reader to develop an intuition for abstract machinery)
Which books is better for a classically-minded reader who is interested mostly in classical algebraic geometry, but wants to understand the modern approach? (possibly, Hartshorne? As he himself says in the preface that he is the classical algebraic geometer, and his books contain a review of classical AG and 2 chapters of applications of the machinery to classical questions, in particular, study of curves and surfaces)
I hope this thread and possible answers could be a useful resource for those starting learning algebraic geometry for the first time.