Here is a list of books that I would recommend for those interested in reading about the Catholic Church. For practical purposes I have tried to name only books that are currently in print. Of course, nowadays many out of print books can be found online.
The Bible is, of course, at the top of any list but special attention should be paid to the Acts of the Apostles and the Letters of St. Paul if you are interested in the history of the early Church.
The three great Christian apologists of the last century were Hilaire Belloc, G.K. Chesterton, and C.S. Lewis. Belloc is not highly regarded by historians today but his historical works are full of great insight and passionate Catholicism. Chesterton's two great works were "Orthodoxy," and "The Everlasting Man." Both were written before he converted to Catholicism but were the source of many conversions.
C.S.Lewis never converted to Catholicism but no Catholic should be unfamiliar with his work, whether scholarly, apologetic, inspirational, science fiction, or children's fantasy. Aside from his most well known works like, "The Chronicles of Narnia," or the science fiction trilogy, my personal favorite is "A Preface to Paradise Lost," (especially the latter half beginning with the chapter on "The Unchanging Human Heart"). I also recommend his contribution to the Oxford History of English Literature entitled, "English Literature in the 16th Century." Catholic readers will enjoy the book's introductory essay, "New Learning and New Ignorance," as well as his discussion of the first translations of the Bible into English. Finally, if you can only read one book on this list, read his, "Mere Christianity."
For the early history of the Church I recommend "The Ancient City," by the great French 19th century historian, Numa Denis Fustel de Coulanges. Read the first 100 pages for an understanding of the real religion of ancient Greece and Rome, and then skip to the last chapter,"Christianity changes the Condition of Government," where Fustel brings out the radical effect of Christianity on the Ancient world. A modern book that does much the same thing is Rodney Stark's," The Rise of Christianity," an extremely readable and provocative sociological study of the reasons for the success of early Christianity.
For the Middle Ages I can think of no better introduction than the work of another outstanding 19th century French historian, Emile Male. In three great works on the religious art of the 12th, 13th, and 14th centuries, Male rediscovered the meaning of Medieval art. The second volume in the series is in paperback form under the title, "The Gothic Image." I would also highly recommend Dorothy Sayers' translation of Dante's Divine Comedy for her brilliant introductions to the three paperback volumes. Even if you find it difficult reading Dante, it would be worthwhile to read her footnotes. By the way, Sayers was an equally gifted contemporary of C.S. Lewis and J.R.R. Tolkien and her detective stories are still worth reading. Monasticism was a central feature of the Middle Ages and a careful reading of "The Rule of St. Benedict" is the best place to start for an understanding of this institution.
For an introduction to the Renaissance and Reformation I recommend the essay by C.S. Lewis," New Ignorance and New Learning," mentioned above. For the Reformation read "The Imitation of Christ," the great spiritual classic usually attributed to Thomas a Kempis. This little book became the world's first best seller after the invention of the printing press and influenced reformers both Catholic and Protestant For the Catholic reformers see "The Autobiography of St. Teresa of Avila," and "St. Ignatius Loyola, the Pilgrim Years," by Fr. James Brodrick, S.J.
The great central issue in the Reformation was the Mass. For an understanding of the liturgical reforms of the Council of Trent see "The Mass of the Roman Rite," by Fr. Joseph A. Jungmann, S.J. For a shorter overview of the Tridentine Mass I recommend the introduction by Fr. F. X Lasance to "The New Roman Missal," one of the best of the Latin-English missals that became so popular in the first half of the 20th century.
For other controversial issues of the Early Modern era, see B. Netanyahu, "The Spanish Inquisition," a balanced and exhaustive study by a great Jewish scholar. I also believe that George Bernard Shaw's introduction to his play, "St. Joan," gives some valuable background on the Inquisition. Arthur Koestler's, "The Sleepwalkers," is a readable account of the beginnings of the conflict between science and religion. The chapters on Copernicus and Galileo are eye opening.
The era of the American and French revolutions was not a period friendly to Catholicism. In Ireland and England Catholics were brutally suppressed. The French revolution sought to destroy the Church in France and in conquered Italy. Catholic Poland was partitioned by powerful enemies. As usual the conquerors wrote the histories. One has to read between the lines to discover the real state of the Church during this era. Unfortunately, one of the best sources for Catholic history and biography is now sadly out of print. I am referring to the great "Catholic Encyclopedia," published in many volumes in the early part of the 20th century with extremely learned articles on every aspect of Catholicism. However, it is available on line.
The Age of Revolutions was followed by the so-called Romantic era, a political, cultural, literary, and artistic reaction against the excesses of the revolutionists. Christianity, especially Catholicism experienced an explosive recovery. Literary giants like Victor Hugo and Fyodor Dostoyevsky turned to religious themes. Hugo's "Les Miserables" has become a classic but I must confess that I like the Broadway play better. Dostoyevsky was not a friend to Catholicism, but his novels, "Crime and Punishment," "The Idiot," and "The Brothers Karamazov," should be on any reading list for Catholics.
For the American Catholic experience I recommend another provocative sociological and extremely readable work by Rodney Stark and Roger Finke, "The Churching of America." The chapters on Catholicism are especially interesting. For missionary activity in America see Paul Horgan's, "The Great River, the Rio Grande in American History," a study of the American Southwest. His chapter, "The Desert Fathers," details the incredible work of the early Franciscan missionaries.
Finally, let me conclude with a short list of 20th century novelists. From America I like Walker Percy, especially," Love in the Ruins." The two outstanding English novelists were Evelyn Waugh and Graham Greene. Waugh's "Brideshead Revisited," was made into an excellent TV miniseries. I don't know if Greene remained Catholic to the end but his early Catholic novels like "The Power and the Glory," are extremely powerful. On the lighter side I heartily recommend his "Monsignor Quixote," which was made into an outstanding film starring the late Alec Guinness. Alexander Solzhenitsyn is the greatest writer of our time and his novels and histories should live forever. As an historian I found his "August, 1914," incredibly moving. Italy has also produced a great Catholic masterpiece. Eugenio Corti's, "The Red Horse," set in Italy during the Second World War can stand in comparison with Tolstoi's, "War and Peace." Sadly, I believe that another Italian masterpiece is now out of print. I am referring to the series of books written after the War by Giovanni Guareschi about the most lovable priest in all literature, Don Camillo. If you can find these at library discard sales the first in the series, "The Little World of Don Camillo," and the last, "Comrade Don Camillo,"