One way to walk through the Old Testament and see Jesus is to ask how the characters and patterns anticipate Jesus by comparison and how they anticipate him by contrast. Similar to the negatives-and-pictures of the old film process, sometimes these people and patterns reveal what Jesus will be like and sometimes they reveal what he will not be like or how much better he will be.
Take Adam, for example. Like Jesus, he is responsible to represent humanity before God. Like Jesus, he is called to cultivate God's creation and to bring about God's perfect plan for mankind. Like Jesus, he had to bear the curse of sin and be banished from God's presence. In Adam's call, we see God's call of Jesus. In Adam's banishment, we see Jesus on the cross and in the grave. This is seeing Jesus in the positive comparison of an old testament character. The ultimate reason for Adam's role was to anticipate the greater role of Jesus.
We also see Jesus in contrast to Adam. Unlike Jesus, Adam surrendered to the lie of Satan and disobeyed and disbelieved God. Unlike Jesus, Adam sought to transfer responsibility for his role to someone else (Eve) and did not want to shoulder it himself. Unlike Jesus, Adam was cursed because of his own sin rather than becoming a cursed exile only as a substitute for others. Frequently, when we see a character in the Old Testament showing contrast to Jesus, they are simultaneously revealing the need for Jesus' salvation that anticipates our condition as well. Like Adam, more than that, in Adam, we desperately need a Savior.
In comparison and contrast, thinking about Adam helps us to see the calling and perfection of Jesus Christ and the prefect Savior he is for us.
A Christian reading Genesis 1-3 should not just be thinking, "What an interesting historical story..." or even "how should I be like or unlike Adam?". Those thoughts are not wrong--but they should progress to the ultimate meditation: "How should I respond to the picture of Jesus that I see here?"
