Start with the Gospels (the first 4 books of the New Testament) then the Acts of the Apostles.
Here's some favorite verses:
Romans 3:23, “For all have sinned, and come short of the glory of God”
Mark 1:15, “The time has come,” he said. “The kingdom of God has come near. Repent and believe the good news!”
Ephesians 2:8-9, “For it is by grace you have been saved, through faith—and this not from yourselves, it is the gift of God— not by works, so that no one can boast.”
John 3:3, Jesus replied, “Very truly I tell you, no one can see the kingdom of God unless they are born again.”
John 3:16, “For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life.’
2 Peter 3:9, “The Lord is not slow in keeping his promise, as some understand slowness. Instead he is patient with you, not wanting anyone to perish, but everyone to come to repentance.”
Acts 4:12, “Salvation is found in no one else, for there is no other name under heaven given to mankind by which we must be saved.”
Romans 6:23, “For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord.
1 John 1:9, “If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness.”
Hebrews 9:27, “And as it is appointed unto men once to die, but after this the judgment:”
Romans 5:8, “But God demonstrates his own love for us in this: While we were still sinners, Christ died for us.”
Matthew 7:21–23, “Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom of heaven, but only the one who does the will of my Father who is in heaven. Many will say to me on that day, ‘Lord, Lord, did we not prophesy in your name and in your name drive out demons and in your name perform many miracles?’ Then I will tell them plainly, ‘I never knew you. Away from me, you evildoers!’
1 Corinthians 6:9-10, “Do you not know that wrongdoers will not inherit the kingdom of God? Do not be deceived: Neither the sexually immoral nor idolaters nor adulterers nor men who have sex with men, nor thieves nor the greedy nor drunkards nor slanderers nor swindlers will inherit the kingdom of God.”
Matthew 3:8, “Produce fruit in keeping with repentance.”
Romans 10:9-10, “If you declare with your mouth, “Jesus is Lord,” and believe in your heart that God raised him from the dead, you will be saved. For it is with your heart that you believe and are justified, and it is with your mouth that you profess your faith and are saved.
2 Corinthians 5:17, “Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things are become new.”