I use different translations but mostly the NIV. No denomination or writer, just stating what God, the Law of Moses, Prophets, Jesus and the apostles said. In reference to what denominations teach, I can’t tell you as I have not read any official statements from them. I have gleaned from talking about Jesus to my customers and people I see throughout the day, what they think about the Good News of Jesus that I tell them. Most don’t understand what He did on the cross other than along the lines of what you said, “That “Christ died for our sins”. Other than that statement they can’t really explain what that means and how it really affects them. Other than they believe they are forgiven.
2 Cor 5:21 God made him who had no sin to be sin for us, so that in him we might become the righteousness of God.
Gal 3:13 Christ redeemed us from the curse of the law by becoming a curse for us, for it is written: "Cursed is everyone who is hung on a tree.
Isa 53:4 Surely he took up our infirmities and carried our sorrows, ( “He took up”, shows purpose ) yet we considered him stricken by God, smitten by him, and afflicted. 5 But he was pierced for our transgressions, he was crushed for our iniquities; (the purpose was for our sins ) the punishment that brought us peace was upon him , (the people involved in killing Him did not know this was what was happening, God did, it was His plan) and by his wounds we are healed. 6 We all, like sheep, have gone astray, each of us has turned to his own way; and the Lord has laid on him the iniquity of us all. (Again purpose, the Lord has laid on him our iniquity, sin) Isa 53:10-11 Yet it was the Lord’s will to crush him and cause him to suffer, and though the Lord makes his life a guilt offering , (this shows that it was the Father’s intention to execute Jesus in our place and to cause Him to suffer ) he will see his offspring and prolong his days, and the will of the Lord will prosper in his hand. 11 After the suffering of his soul,(His soul, the man Jesus, suffered) he will see the light [of life] and be satisfied; by his knowledge my righteous servant will justify many, and he will bear their iniquities.( The Son of Man was the corporate head of mankind who came for this purpose, to bear their iniquities)
The following scripture shows purpose and plan from the beginning. Rev 13:8 all whose names have not been written in the book of life belonging to the Lamb that was slain from the creation of the world.
So it was the Father’s will to make Jesus sin, so that through God’s judgment on Him, God judged sin. Then He was resurrected to true life, so those who fully lean on Jesus for help and safety, will be freed from their slavery to sin and the devil. The inward, the true man Jesus became sin, died in sin, was consumed by true death, was judged and then rose up from death to life. I’m not talking about His body at all at the moment, just the inward man. The death He died was to sin so that we would die to sin. When He rose, He was the First Born from the dead. Others had risen like Lazarus, but it was not the same kind of resurrection. Jesus was consumed by death, but when He raised it was unto true life. He was freed from true death and sin, all who trust and continue to trust Him, are freed from sin and true death.
Now those who trust in His cross, go through that with Him as a part of the Son of Man, our corporate head. And now we are Born Again by the Father’s will. Jesus said what is born of the spirit is spirit. It is the spirit of the man, the true man, that is Born Again, a New Creation, united to the First Born from the dead.
Col 3:1 Since, then, you have been raised with Christ, set your hearts on things above, where Christ is seated at the right hand of God. 2 Set your minds on things above, not on earthly things. 3 For you died, and your life is now hidden with Christ in God. 4 When Christ, who is your life, appears, then you also will appear with him in glory.