After memorizing the Sermons on the Mount, my long-term goal for verbatim memorization of the Bible is to memorize the Psalms and the Epistles. The Psalms will come after the Epistles, though I have a few of them memorized, but for now I'm hitting the Epistles.
I'm well into Philippians chapter 4 and fully expect to complete it in October. It has been a slower journey for me as I work out how I best memorize. I've settled on a method and am chugging along just fine at about a verse a day.
I've spoken with a lot of people about what my next book should be. Among people who do not memorize I've had an overwhelming response that it should be Romans. Somehow, that doesn't feel right. Romans seems like it should be the last Epistles to be memorized after the other Epistles are in your head, supporting you as you memorize.
For me, the book I'm most attracted to memorizing is Hebrews. Almost no one uses it in theological discourse, though it is theologically deep, and it has a lot to say about the OT. I feel this book is a good one to mull over for a long while, reading books on it and contemplating it over and over, especially in relation to the other Epistles. Plus, it would be interesting to have it in your mind while reading the OT.
I'll keep you posted once I finish Philippians 4.