One of my favorite books from the Tanakh is Ecclesiastes. It's a very poetic book where the author muses about the meaning of life and death, and at the end of it comes out with the conclusion that there isn't much of a meaning to life besides enjoying what you have and believing in God. It's the origin of many commonly used phrases in the English language (e.g. "nothing new under the sun") and is a beautiful book to read.
The Song of Solomon is beautiful too, and one verse, ani l'dodi, v'dodi li
(I am my beloved's, and he is mine) has special significance for me and many others because it's used as the "I do" by Jewish women such as my wife in non-Orthodox wedding ceremonies (in Orthodox practice only the man speaks). Leviticus is a bit of a bore for me, to be honest, as it's just a set of laws.
I have to say I've never read that much of the Christian New Testament because I just find in many cases it makes me viscerally angry. I recently tried reading it again as I went along to a "Jewish perspective on the New Testament" reading group at my synagogue and I only went along to one class as after reading the Gospel of Matthew I came to the conclusion that I found the narrative in that book incredibly spiteful towards Jews and that the overall portrayal of Jews and Judaism throughout the NT was highly negative. I suppose it's the same kind of feeling many non-Jews may have when reading the Christian Old Testament.