I've been gorging myself on the books of Matthew and Isaiah lately. Both are absolutely phenomenal. One of the things I've been noticing in my studies is that, especially in the Gospels, there is, in our contemporary Christianity, a tremendous lack of contextualization when we go to understand the life and the words of Jesus. We think of the four Gospels as repositories of fragmentized selections of Jesus' ministry. Rather than approaching Matthew, for example, as a historical literary narrative on the teachings and life of Jesus with consistent flow, character, and internal harmony, we approach it almost as if it were a chronologically-arranged newspaper in which each event is not readily expected to correlate with the next. Regrettably, we have learned to comprehend the Bible as a compendium of individual verses or passages. With the exception of portions of Proverbs, none of the books of the Bible were written or intended to be understood this way.
So, in short, here is my suggestion for you: start reading whole books of the Bible, totally ignore chapter and verse divisions (which are not original to the Biblical writings and were added in the 1500s), read for natural literary divisions instead, and perhaps purchase a copy of The Books of the Bible edition to assist you in reading a book of the Bible more objectively.