As you read Genesis, you may notice that after the fall each new character which is introduced seems to be presented to raise our hopes that this one is the seed which God promised Eve. Cain, Seth, Noah, Abram, Ishamael, Isaac, Jacob and so on. The hope is raised that each one may be the deliverer which God promised, but each time, some way or another, they are revealed to be “not the one.”
Cain seems like the obvious answer to God’s promise, but turns out to be quite the opposite. Noah is like a new Adam, but in the end we see that though he was a righteous man, he was only a symbol of the true deliverer God had promised. On it goes, with either our hopes being disappointed by the sin of the man, or by God’s revelation that His promised Messiah would come through the seed of the elected person.
A very simple blessing of reading the OT and NT simultaneously is that as you read the stories of the patriarchs, you are reading the Gospel of He Who was indeed God’s Promised One. Matthew presents Jesus as the long-awaited King, and then shows how those to whom the promise of God’s kingdom had come reject the King He had sent to deliver them.
Finally, a big picture encouragement regarding reading the Scriptures. As the Westminster Confession teaches, the Scriptures make a “full discovery” of the “only way of man’s salvation (Chapter I.5).” This provides abundant evidence that it is in fact God’s Word. However, the only means of full persuasion of the Bible’s authority is a something the Holy Spirit gives. In essence, we don’t run a mental investigation and at the end go, “Well, logically I’ve concluded this is God’s Word.” This puts man in judgement over the Word of God. Rather, after the Holy Spirit miraculously vivifies our heart, we are given assurance that God has proclaimed salvation to us through His Word. The Bible isn’t an academic text, it is tidings of salvation for those who have ears to hear. Ears that have been miraculously opened by God’s Holy Spirit.