There are several lists of Favorite verses on the Internet. Here are just a few of them. If you are going to start memorizing Scripture, then these might be a good place to start. Oh, and a little hint about memorization. Did you know it is easier to memorize Scripture from a version that is not in every day English? If you read from NIV, or similar, you might consider memorizing from NASV or KJV. Your brain remembers the older English better! (Years of Bible quizzing brought me to this knowledge.)
BIBLE GATEWAY is the best online source for comparing of verses. You can quickly look up any verse in any version.
Top 20 Bible Verses to Memorize
Joshua 1:9: Have I not commanded you? Be strong and of good courage; do not be afraid, nor be dismayed, for the Lord your God is with you wherever you go.
Isaiah 40:30-31: Even the youths shall faint and be weary, and the young men shall utterly fall, but those who wait on the Lord shall renew their strength; they shall mount up with wings like eagles, they shall run and not be weary, they shall walk and not faint.
Isaiah 53:5: But He was wounded for our transgressions, He was bruised for our iniquities; The chastisement for our peace was upon Him, and by His stripes we are healed.
Proverbs 3:5-6: Trust in the LORD with all your heart, and lean not on your own understanding; In all your ways acknowledge Him, and He shall direct[a] your paths.
Jeremiah 29:11: For I know the thoughts that I think toward you, says the Lord, thoughts of peace and not of evil, to give you a future and a hope.
John 3:16: For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life.
John 14:6: Jesus said to him, “I am the way, the truth, and the life. No one comes to the Father except through Me.
Romans 3:23-24: For all have sinned and fall short of the glory of God, being justified freely by His grace through the redemption that is in Christ Jesus.
Romans 5:8: But God demonstrates His own love toward us, in that while we were still sinners, Christ died for us.
Romans 8:28: And we know that all things work together for good to those who love God, to those who are the called according to His purpose.
Romans 12:1-2: I beseech you therefore, brethren, by the mercies of God, that you present your bodies a living sacrifice, holy, acceptable to God, which is your reasonable service. And do not be conformed to this world, but be transformed by the renewing of your mind, that you may prove what is that good and acceptable and perfect will of God.
Galatians 2:20: I have been crucified with Christ; it is no longer I who live, but Christ lives in me; and the life which I now live in the flesh I live by faith in the Son of God, who loved me and gave Himself for me.
Galatians 5:22-24: But the fruit of the Spirit is love, joy, peace, longsuffering, kindness, goodness, faithfulness, gentleness, self-control. Against such there is no law. And those who are Christ’s have crucified the flesh with its passions and desires.
Ephesians 2:8-9: For by grace you have been saved through faith, and that not of yourselves; it is the gift of God, not of works, lest anyone should boast.
Philippians 4:13: I can do all things through Christ who strengthens me.
Philippians 4:5-7: Let your gentleness be known to all men. The Lord is at hand. Be anxious for nothing, but in everything by prayer and supplication, with thanksgiving, let your requests be made known to God; and the peace of God, which surpasses all understanding, will guard your hearts and minds through Christ Jesus.
Philippians 4:8: Finally, brethren, whatever things are true, whatever things are noble, whatever things are just, whatever things are pure, whatever things are lovely, whatever things are of good report, if there is any virtue and if there is anything praiseworthy—meditate on these things.
2 Timothy 3:16-17: All Scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness, that the man of God may be complete, thoroughly equipped for every good work.
1 Peter 3:15-16: But sanctify the Lord God in your hearts, and always be ready to give a defense to everyone who asks you a reason for the hope that is in you, with meekness and fear; having a good conscience, that when they defame you as evildoers, those who revile your good conduct in Christ may be ashamed.
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.