As someone in the same boat as you:
First of all, the Catechism and the Bible. I’m assuming you covered these in RCIA, but if you didn’t, or only covered them partially, you should complete these two books before moving on to anything else. After you’ve read the Catechism and the Bible you’ll already know more about Catholicism than 90% of the people sitting in the pews will. Yes, the task of reading the entire Bible seems daunting, but believe me, it’s worth it. Start out with the Gospels, then the rest of the New Testament, then the Old Testament. Some people like to start the OT with the psalms and prophets as these are where most of the Messianic prophecies are from; but, as far as the psalms go, you should ideally have a good psalter that you pray regularly from anyways.
Once you’ve got these two down pat, it’s really a question of what you want to get into. Fulton J. Sheen, Scott Hahn and Benedict XVI (most of his books are published under his original name of Cardinal Ratzinger) all do great jobs explaining the faith, and they’ve all published books on a variety of subjects. Fulton J. Sheen’s Life of Christ and Pope Benedict’s Jesus of Nazareth series are considered the books par excellence on the life of Christ. Other good titles by them include Three to Get Married and Hail, Holy Queen, which do great jobs at explaining the Catholic stances on Marriage and Mary, respectively. The Lamb’s Supper is also considered a spiritual classic, that will let you see the Mass in a whole new light.
If you want to get more into Theology, Benedict XVI published a number of good books on the subject. Another title that I’d recommend is “Theology For Beginners” by Frank Sheed, and “Orthodoxy” and “The Everlasting Man” by G.K. Chesterton.
If you want to get more into Prayer, the books I’d recommend are a Psalter, A Daily Missal, and the LOTH (there are also many abbreviated LOTH books that are cheaper than the full volume set). An Eastern Horologion is quite a monumental task to pray but well worth it if you can find the time. It should be noted, that most all of these resources can be found online; I’ll post the links later on.
If you want to get more into Hagiography, the book par excellence is Butler’s Lives of the Saints, but it’s four volumes and will cost you an arm and a leg. If you want to stay at a small book length, some recommended titles are Story of a Soul by St. Therese of Lisieux, Augustine’s Confessions, the autobiography of St. Teresa of Avila, and Seven Story Mountain by Thomas Merton (technically, he’s not a saint, but it’s still an excellent insight into one of the greatest minds in Modern Catholicism).
If you want to get more into contemplative/mystical Theology, the writings of St. John of the Cross, St. Teresa of Avila and Thomas Merton will be enough to engage you for quite a while.
If you want to try your hand at Centering Prayer, then Open Mind, Open Heart and The Cloud of Unknowing. The books of contemplative/mystical theology are also recommended. (DISCLAIMER FOR THE MODS: While I know that discussion of Centering Prayer isn’t allowed, I think an exception could be made for a simple book list. If not, I’ll be happy to edit the post and remove it).
If you want to get into Philosophy, then the City of God and Aquinas’s writings are what you want to get. Get a summary of Aquinas’s works (several are available) rather than a full multi-volume set of his books.
If you want to get more into Bible Study, get a study Bible. The Navarre Study Bible is generally regarded as the best, but it’ll cost you an arm and a leg. The Ignatius Study Bible is excellent, but it’s a work in progress; currently only the New Testament and a few of the OT books are out. Haydock’s Douay-Rheims Commentary is also excellent, but quite dated and difficult to find. The NAB bible has extensive footnotes, and most other Catholic Study Bibles you’ll find are simply rebranded NABs. The NJB also has a study edition with extensive footnotes.
Two more notes. One book everyone should have is The Imitation of Christ; Catholic tradition holds that this is the second-best selling book in the world after the Bible. Another great author, whose is not Catholic but whose books are widely regarded as non-denominational is C.S. Lewis. Mere Christianity, The Screwtape Letters and Reflections on the Psalms are all recommended titles.
Some links you’ll find useful:
The full Liturgy of the Hours:
divineoffice.org/
A (greatly abbreviated, which is still extremely long) Horologion:
orthodox.seasidehosting.st/hourly_services
Christian Classics Ethereal Library (this contains most of the Christian classics from before the 20th century):
ccel.org/
Haydock’s 1859 Commentary:
haydock1859.tripod.com/