One thing I've never understood is 'Jesus died for our sins'
If you’re looking for Jesus’ own idea, you have to decide how much you trust the Gospels. Throughout the latter part of his ministry, he seems to expect to die. There’s no strong theology associated with it, but a kind of general understanding that being true to his calling will inevitably cause him to be killed. The very lack of a traditional doctrinal explanation gives support support to the accuracy of this.
Interestingly, Calvin’s treatment of the atonement starts with this. You can see it in C S Lewis’ novel “That Hideous Strength,” where Mark first starts to understand Christianity, as the straight collides with the broken world.
The most explicit explanation he gives is in the words of institution at the Last Supper. These are duplicated in 1 Cor. (This multiple attestation says that the words are very early.) He says “this is my blood of the new covenant.” Most interpreters think the new covenant is a reference to Jer 31:31, where God makes a new covenant, writing the Law into our hearts. This is consistent with Jesus’ whole message, which deemphasizes the Law and emphasizes basing our lives on love of God and neighbor. Blood of the covenant is, of course, a reference to Exodus 24:8. That suggests that Jesus saw his death as in some sense a covenant sacrifice, intended to create a new beginning.
Jesus was concerned throughout his ministry with the future of his people. He foresaw disaster if they couldn’t overcome their belligerence and turn to forgiveness. He saw himself as God’s agent in establishing God’s rule, but also I think as his people’s representative. Given Jewish backgrounds of redemptive death, I think it’s reasonable to suggest that he saw his death as, in part, repentance on behalf of his people, and an attempt to turn them away from the path that eventually led to the disaster of 70 AD.
I don’t accept the typical Christian view that God hates sin so much and we're such terrible sinners that someone has to pay, even if it’s an innocent victim. I think God can and does forgive. Hence I see Jesus’ death, first, as a consequence of loyalty to his mission, and second, as a attempt to change people. I think in Rom 6 Paul gives an interpretation that is his version of this, though with theological developments beyond Jesus' own words.