Which ever translation you end up choosing, Delighting In Grace, please do not read your Bible front to back, or Genesis to Revelation. The Bible was not meant to be read this way.
The Old Testament is divided into 3 parts, but you will find that your Bible does not keep the order. First, the Law, which includes the books of Genesis, Exodus, Leviticus, Numbers, and Deuteronomy. Second, the Prophets, beginning with "major" and ending with "minor," or the "former" and "latter." The books of the Prophets are as follows: Joshua, Judges, 1 Samuel, 2 Samuel, 1 Kings, 2 Kings, Isaiah, Jeremiah, Ezekiel, Hosea, Joel, Amos, Obadiah, Jonah, Micah, Nahum, Habakkuk, Zephaniah, Haggai, Zechariah, and Malachi. The last 12 are considered the "minor" Prophets. Lastly, the Writings: Psalms, Proverbs, Job, Song of Songs (or Solomon), Ruth, Lamentations, Ecclesiastes, Esther, Daniel, Ezra, Nehemiah, 1 Chronicles, and 2 Chronicles. This is the exact order that the Jews use. Our English Bibles do not follow this order.
The New Testament has no real order past the Gospels and the Acts, and Revelation being last. The order of the New Testament is fine as is, but I PERSONALLY would switch up the order of the Gospels a little bit. I would keep Matthew first. The Gospel of Matthew is the longest and most in depth. I would then go with John. John is different than all of the other Gospels, and gets more personal with Jesus. I would then go Mark. Mark is the shortest Gospel and confirms what Matthew says, and will confirm what Luke says next. I would read Luke last. The author of Luke is also the author of Acts, which is directly after the Gospels. This will be evident immediately, as he writes to Theophilus again. Mark will also still be freshly in your mind by the time you get to Acts, as you read it just before Luke, and what Jesus said in "the longer ending" of Mark, regarding speaking in other tongues, will appear right away in Acts.