Salvation turns on exactly what you have laid out from Romans 10: believing in the heart that God raised Jesus from the dead and confessing with the mouth that Jesus is Lord. That is not a formula to repeat lightly; it is the surrender of your whole life. A living faith does not merely nod at a truth, it reorders everything. The One you confess as Lord is the One before whom every knee will one day bow, in heaven, on earth, and under the earth. When that day comes, the confession will be forced, and it will not bring salvation. To confess him now, willingly, while grace is still extended, is what saves. That is why Scripture pleads, now is the accepted time; now is the day of salvation. Do not let it pass.
Jesus himself is the captain and perfecter of this salvation. He did not stand aloof from the cost. Though he was in the form of God, he emptied himself, took the form of a servant, and learned obedience through the things he suffered. His obedience took him to the cross, and through that suffering he became the author of eternal salvation to all who obey him. That does not mean we earn salvation by our performance. It means that genuine faith embraces the same posture of yieldedness. If you believe him, you will follow him. A faith that refuses to obey is not saving faith, it is dead, as James reminds us. Abraham believed God, and that belief was counted as righteousness, but the belief was not empty words; it moved his feet.
What you said about turning from sin is vital. Repentance is more than regret. Many are sorry for the mess sin has made, but that is a worldly sorrow that produces only death. Godly sorrow, on the other hand, works a change. It brings forth fruit that demonstrates a new direction, a clearing of oneself, a holy indignation against the old ways, a zeal for what is right. When Jesus began to speak of this great salvation, his forerunner called people to a baptism of repentance, a death to the old life. The axe was laid to the root. The call was not to trust in ancestry or religious habit but to produce fruit that matches a changed heart. That fruit does not add to Christ’s finished work; it simply proves that the heart has truly turned.
So hear this clearly: nothing you do can make God owe you salvation. The law was never given as a ladder. The promise rests on grace alone, received by faith alone. Yet that faith never remains alone. Working out your own salvation with fear and trembling does not mean working for it in panic, as though Christ’s work were insufficient. It means living out the gift with deep reverence, knowing that it is God who works in you both to will and to do his good pleasure. All the effort that produces a godly life is the evidence that he has already laid hold of you.
Your instinct to go to the Gospels is right. Start in John, as you said, and meet Jesus as the Word made flesh, the Lamb of God who takes away the sin of the world. See him lay down his life and take it up again. See Thomas fall before him and cry, “My Lord and my God!” That is the confession of salvation. That is the allegiance of a life. Hold fast to that confession, for we have a great high priest who has passed through the heavens, Jesus the Son of God. He is not untouched by our weaknesses; he was tempted in all points as we are, yet without sin. He knows the struggle. He is able to save to the uttermost those who draw near to God through him.
Do not delay. The grace of God that brings salvation has appeared to all men. The open door stands before you now. Believe in your heart that God raised him from the dead. Confess with your mouth that Jesus is Lord. Turn from your sins and follow him. In doing that, you receive eternal life, not a future hope that trembles, but a present possession sealed by the Spirit. Read, pray, and walk in the light of his word. He who began a good work in you will carry it on to completion.