All of the books mentioned so far are excellent, but some are rather weighty and heavy and even a little frightening.
E.g., I love the book, The Imitation of Christ, by A Kempis, but had I read it as a non-Catholic, I think I would have been scared away from Catholicism. It’s too heavy for a non-Catholic who doesn’t possess a full understanding of Catholic theology. Without that understanding of Catholic theology, the book becomes a paeon for “salvation by good works,” which can be a real turn-off to non-Catholics.
I agree with the Thomas Howard recommendation, and add his great book, Evangelical is Not Enough.
I also suggest anything by Dr. Scott Hahn. Rome Sweet Home is great, but try is other books–anything by the man is well-written and easy-to-understand!
Crossing the Tiber by Steve Ray specifically delves into the Catholic doctrines of Baptism and Eucharist. (He’s a former Baptist.)
I like Catholicism and Fundamentalism by Karl Keating. The LDS is not considered a “fundamentalist Christian” church, but I think you would still enjoy a lot of the information in this book.