Hi Sarah
I will refer you to the book The Truth of the Cross by RC Sproul. It is a fantastic book on the atonement of Christ.
Here is an excerpt from the book that is pertinent to this thread:
Just as there are three basic types of theology, there are three basic views of the atonement with respect to its necessity historically. First, there are those who believe that an atonement is absolutely unnecessary. The Pelagians in all their forms fall into this category. Pelagianism, originating in the fourth century; Socinianism, which arose in the sixteenth and seventeenth centuries; and what we would call liberalism as a distinctive theology today are all essentially non-Christian because at the heart of each is a denial of the atonement of Jesus Christ. These schools of thought, by taking away the reconciling action of Christ from the New Testament, are left with nothing but moralisms. For them, the cross is where Jesus died as a moral example for men. They view Him as an existential hero, as One Who brings inspiration to us by His commitment and devotion to self-sacrifice and to His humanistic concerns. But these moralisms are anything but unique and hardly worthy of allegiance. In Pelagianism, there is no salvation, no Savior, and no atonement because in Pelagianism no such salvation is necessary.
Second, there are those who believe an atonement is only hypothetically necessary. This view historically expresses the idea that God could have redeemed us by a host of ways and means, or He could have chosen to overlook human sin. However, He did something dramatic when He committed Himself to a certain course of action. He chose to redeem us by the cross, by an atonement. Once He committed Himself, it became necessary, not de jure or de facto, but de pacto—that is, by virtue of a pact or a covenant that God made by issuing a promise that He would do a particular thing. The promise was gratuitous in that it was not necessary for Him to do it, but He nevertheless made the promise. He was then committed to that course of action. That's what is meant by a hypothetical necessity for an atonement.
The third view, which is the classical, orthodox Christian view, which I am convinced is the biblical view, is that an atonement was not merely hypothetically necessary for man's redemption, but was absolutely necessary if any person was ever going to be reconciled to God and redeemed. For this reason, orthodoxy has held for centuries that the cross is an essential of Christianity, essential in the sense that it is a sine qua non, "without which it could not be." If you take away the cross as an atoning act, you take away Christianity.
In regards to ransom, though, he talks about the concept of redemption. The concept of ransom stands behind the broad biblical term redemption. The concept of redemption is reflected in Scripture particularly in the book of Ruth. A redeemer is one that takes action to set another free. God was Israel's redeemer when he delivered them from Egypt. Exodus is a story about redemption.
Here is another excerpt from the book:
That brings us back to the cross, where Jesus made atonement for His people, satisfying the requirements of God's justice. As we have seen, the atonement is a multifaceted event - Jesus is shown providing surety for our debt to God, mediating the enmity between us and God, and offering Himself as a substitute to suffer God's judgment in our place. But He is also seen in the New Testament as the Redeemer, the One Who redeems His people from captivity, setting them free by offering Himself as a ransom.
There's a lot more material in this book and it would be great to have in your library. I could review it a little more if the above doesn't satisfy your question.
One point he makes is that some hold the opinion that the "ransom" was paid to Satan, but he does not agree with this view. The offense concerning sin is to God, so the "payment" was made to God, not Satan.
