The words you shared from Romans 10 are the very heart of the matter. Salvation is not a distant hope or a riddle to be solved; it is a gift received when a heart truly believes. Confessing Jesus as Lord with your mouth and believing in your heart that God raised Him from the dead, that is the narrow door that opens into eternal life. The righteousness God accounts to you is not something you earn; it is imputed to you through faith, just as it was with Abraham when he believed God. So you have already seized on the essential truth.
Now, the faith that saves is never a bare statement. True faith in Jesus Christ will always produce a changed life. This does not mean that your works add anything to your salvation or make you more acceptable to God. You are saved by faith alone. But the kind of faith that justifies you is a living thing. It breathes and moves. It turns from sin, not to bargain with God, but because the heart now loves what God loves. When John the Baptist called for repentance, he demanded fruit that matched the confession. The same holds for us. If you say Jesus is Lord, then your life will begin to follow His commands, not perfectly, but genuinely. That obedience is the natural fruit, not the root. You will not be perfect, faith often stumbles, and even the strongest believer has lapses, but the direction of your heart will be set on Him.
The fact that you are looking for salvation, that you are drawn to these Scriptures, is itself a work of God. The faith to believe did not originate in you; it is a gift, so that no one may boast. You can never produce it by willpower or reform. You receive it by hearing the word of God, and that is why your instinct to read and study Matthew, Mark, Luke, and John, starting with the book of John, is so wise. Faith comes by hearing, and hearing by the word of God. In those Gospels, especially John, you will see Jesus clearly: His life, His death for your sins, His bodily resurrection. As you read, ask God to open your eyes to see Him as He truly is. The promise is that whoever believes in Him will not perish but have everlasting life.
If you confess with your mouth that Jesus is Lord, make sure that confession is not empty. It is not merely a prayer recited, but the surrender of your whole self, your past, your sin, your mind, and your will, into His hands. That surrender will be demonstrated over time, not by flawlessness, but by a new direction. You may not always feel different; feelings are uncertain. But you can stand on the promise of God, knowing that if your trust is in Christ alone, He has saved you. He is the author and finisher of your faith, and what He begins, He will complete. Keep seeking Him in His word, keep turning from what you know to be sin, and rest in the finished work of Christ, not in your own performance. God, who sees your heart, will account your faith for righteousness.