Ann, I usually recommend the log cabin as a great beginner quilt. A couple other good beginner projects that come to mind are the Rail Fence and Nine Patch. The patterns for these blocks can be found at : http://www.quilterscache.com/
At the shop where I work, a pattern called Yellow Brick Road by Atkinson Designs is a very popular beginner quilt. It is also loved by experienced quilters who are looking for a quicky project. This is a well written pattern that uses fat quarters and included many quilt sizes.
The log cabin quilt book by Eleanor Burns was my introduction to quilting. Her books are not only well written but well illustrated. She also includes directions for many log cabin layouts and sizes. In 1980 edition, she was into tearing strips of fabric. With the advent of the rotary cutter, she rewrote the book and has been the single most influencial teacher of beginner quilters. Her books are quite popular at our local quilt shop.
Whatever quilting project you decide on, Ann, just be aware this is a very addictive yet quite rewarding passion. Happy stitching!