So I have been meaning to learn a little algebraic geometry for some time now, but have never gotten around to it. Since classes are just now winding down for the year, I figured that it was an ideal time to self-study a bit. Now for a bit about my background: I know that commutative algebra is provides the local tools in some sense for algebraic geometry, and in previous classes I have worked through Introduction to Commutative Algebra by Atiyah and MacDonald as well as Undergraduate Commutative Algebra by Miles Reid. I am hoping that these books provide enough background to begin learning a little algebraic geometry, but if not, then I am not opposed to reading a more voluminous work like Eisenbud's text on commutative algebra. Looking around, most of the common introductions to algebraic geometry seem to be either the book by Hartshorne or the (red) book by Mumford. Are these good places to start or are there other texts that I should look into? I would like to add that the cost of the book is not an issue since I plan on checking them out from my university library.