I think C. S. Lewis's best books are his theological fiction, such as The Great Divorce, The Screwtape Letters, and The Pilgrim's Regress. The first two would be good places to start. The Pilgrim's Regress is good, but difficult - one practically needs a guide book to get through it and understand all of the philosophical and classical allusions (Kathryn Lindskoog wrote such a guidebook called Finding the Landlord). But anyone could read and enjoy The Screwtape Letters or The Great Divorce. Lewis's best qualities as a writer shine like brilliant stars in a constellation in these two books: his skill as a story teller, his powers of imagination, his perceptive insight into the human heart, his stark sense of the beauty of goodness and the horror of evil.
Lewis's essays are also good places to start: The Weight of Glory and God in the Dock are two very good volumes, though there are many more. The post below is from God in the Dock in an essay called "Miracles." A similar passage is also found in Lewis's book Miracles.
Surprised by Joy:The Shape of My Early Life, Lewis's spiritual autobiography, is both brilliant and compelling. In many ways, it is a key to understanding his other writings. It is one of the first books by Lewis I read and one that I return to periodically.
Lewis's books on theology and Christian life, such as Mere Christianity, The Problem of Pain, Letters to Malcolm: Chiefly on Prayer, Miracles, etc. are good in many ways with many exceptional passages - but I also tend to find more to disagree with in these. Lewis was both Arminian and Anglican (nor was he, by his own admission, a trained theologian) so many things he says about certain aspects of theology are problematic. He is best on ethics, aesthetics, and the basic elements of historical Christian orthodoxy (trinity, incarnation, resurrection, etc.), but weaker (in my judgment) on the atonement, questions regarding predestination and free will, and the specifics of soteriology (doctrine of salvation).
Lewis's own field of study was literature, and his essays and books in this category are outstanding, though may be of less interest to beginning readers. His An Experiment in Criticism blew me away fifteen or sixteen years ago when I read it as a teenager. It blew me away again last year when I reread it. His essays collected in Of Other Worlds are entertaining and insightful and the same could be said of many other books and essays relating to literary criticism. I've not read near all of this material, but plan to eventually. Everything I read, I enjoy.
Finally, Lewis's fiction is superb. Perelandra is probably my favorite novel ever, but it comes second in his Space Trilogy, so read Out of the Silent Planet first. Lewis's own favorite from all his books is Till We Have Faces; it is truly a remarkable story. I actually like his Narnian stories less than most of his other writings, but some of these are also quite good. The Voyage of the Dawn Treader is my favorite. That's more of an answer than John asked for, hence I turned it into a post! Hope it helps some aspiring to read C. S. Lewis!