Did Jesus' Death Atone for Our Sins?

We often hear that Jesus died to pay the ransom price for us because of our sins, or Jesus died in our place, or Jesus died as a sin sacrifice to atone for our sins. But are these statements all accurate? There have been throughout history multiple theories on the atonement - and the oldest of these is ignored by the current church, and I will tell you why it's really the best theory and I will tell you why it is often wrongly rejected.
And then the questions comes up, do we really need an atonement? Does it have to be blood? If our sins are forgiven and forgotten through repentance, as God promised, is atonement still needed? Is shed blood required for atonement? And if so, will God accept a human blood atonement? Did God ever really want blood sacrifices in the first place? Or could sins be forgiven without the blood being shed? These questions are all answered by the Scriptures and the results may surprise you, as they did me.