Your heart to see others come to salvation is precious to the Lord, and the Scripture you shared is the very heart of the gospel. Romans 10 says if you confess with your mouth that Jesus is Lord and believe in your heart that God raised Him from the dead, you will be saved. With the heart one believes and is justified, and with the mouth one confesses and is saved.
That promise shows us how salvation happens. It is not by keeping the law or by adding good works to faith. Scripture teaches that all are under sin, so that the promise might be given to those who believe. When a person first believes in Jesus Christ, God accounts that faith as righteousness, before any works have been done. Jesus has opened the door to every blessing God promised, and by faith in Him you enter into that covenant.
This is why our standing before God rests completely on faith in Jesus Christ alone. We are children of God by faith in Christ Jesus. God looks upon those who have trusted in Jesus and sees them in Christ, clothed in His righteousness. That righteousness is complete. You cannot add to it, and you do not need to try to improve it by your own efforts. We are saved by grace through faith, and that not of ourselves. If someone answers that their hope of eternal life is faith in Jesus Christ, they have answered well. The moment we add anything to faith in Christ alone, we move away from the gospel.
Because salvation is through Jesus alone, every person has the same direct access to God through Him. There is one mediator between God and man, the man Christ Jesus. No one needs to come through another person or system. We each come the same way, through faith in Jesus, and our whole past, every sin and trespass, is blotted out through faith in Him.
The confession that Jesus is Lord is more than words. There will be a day when every knee will bow and every tongue will confess that Jesus Christ is Lord to the glory of God the Father, but then that confession will not be unto salvation. Today, to confess Jesus as Lord means to submit your life to His lordship with a faith that comes from the heart. A genuine faith in Jesus will transform the life. We do not do good works to be saved, we do them because we are saved. A true faith will show itself in a changed life, in turning from sin and walking in obedience to Him. If a person says Jesus is Lord but continues to walk after the flesh in disobedience to the Word, that confession is empty. The faith that justifies is a living faith that leads to following Him.
So your encouragement is right and biblical. Call people to believe in their heart that God raised Jesus from the dead, to confess with their mouth that Jesus is Lord, to turn from sin, and to follow and obey Him. And your counsel to read Matthew, Mark, Luke and John, beginning in John, is excellent. John clearly presents who Jesus is, what He has done, and how we receive eternal life through believing in Him. As people read, pray that they will see not only what Jesus did, but who He is, and that they will receive Him and be rooted and built up in Him.
May the Lord use your witness to draw many to trust in Jesus alone for the forgiveness of sins and the gift of eternal life.