TITLE: Path to Basics in Algebraic Geometry from HS Algebra and Calculus?
QUESTION [40 upvotes]: In this question, Why study Algebraic Geometry?, Javier Álvarez, develops a succint but encompassing description of algebraic geometry and its spread across different areas of mathematics. Indeed, it is this very answer that generates this new question:
Initial Question: Is there a coherent path from high school algebra and beginning calculus to the beginning of algebraic geometry? In other words, can one self-study towards algebraic geometry, only assuming a very modest mathematics background?
I understand that what I am asking is highly non-trivial, because it assumes a certain subject mastery and expository command, that I think many mathematicians simply don't possess. (In particular, Reid's book(s) are good, but could be better
Consider that much of high school mathematics rests on calculational arithmetic and algebra, and related analytic and geometric methods that are fairly straightforward. Indeed, it is arguably what supports the calculational, plug and chug with minimal theory that is most college calculus courses. On the other hand there is the more careful and, light but rich, theoretical treatment found with Spivak or Apostol. 
Thus, not assuming that it would be trivial or wholly straightforward, there should be a way of developing a foray into some of the more interesting problems, and then just developing a plan to concurrently back fill any theory. Indeed, a strong foundation for algebraic geometry, for example, and its problems might lend motivation and coherence to the latter end of pre-college through undegraduate mathematics, instead of the current scatter of, typically, unmotivated degree requirements. 
Revised Question: What set or sets of problems in mathematics can serve as a motivational basis for study towards the more sophisticated and abstract results in algebraic geometry?

REPLY [5 votes]: Certainly Javier is a master at blazing a trail in algebraic geometry and wetting your appetite. I think your question is quite pertinent, especially when you have to go it alone (at least for a while). 
In pursuing a similar quest, I ran across a review of this book which looks nice from a standpoint of motivation and laying things out in a context that is accessible. It may be useful to see what lies in store, yet presented in terms that you are familiar with.
Kendig, "A Guide to Plane Algebraic Curves"
http://www.amazon.com/Algebraic-Curves-Dolciani-Mathematical-Expositions/dp/0883853531