My basic birding library would look something like this:
1. Field guide, preferably the big Sibley
2. Kaufman's
Advanced Birding and Sibley's
Birding Basics. These are useful for sorting out tricky identifications and learning how to look at birds.
3. A guide to local birding sites - in addition to the book cited above by crispycreme, there may be information about where to bird available from your local bird clubs or Audubon Societies. Joining a local birding listserve (or looking through its archives online) will help you find birding spots too.
4. A guide to bird behavior: I find Kaufman's
Lives of North American Birds most useful, but Sibley's
Guide to Bird Life and Behavior and Ehrlich's
Birder's Handbook are also good. The main difference between Kaufman and Sibley is that Kaufman treats individual species while Sibley only treats families.
5. Sound recordings: There are reference CDs available from Peterson and Stokes with bird calls, and also the Peterson
Birding by Ear CDs. The Peterson Field Guide on CD-ROM also has audio files but generally the quality is not as good as the music CDs.
Some of these may be available at a substantial discount at
Book Closeouts.
There are also many fine books that treat individual bird families, but you do not really need them right now. As you get deeper into birding, you might look into picking some up through bargain shops, second hand stores, etc. In particular there is a great guide to hawk identification by Dunne, Sibley, and Sutton. The main thing though, when you are starting out, is to get out in the field and look at birds and listen to them. Sketching is a great idea, as is writing out full descriptions noting every detail and then comparing them with the field guides at home.