Gen. 3:15 - we see from the very beginning that God gives Mary a unique role in salvation history. God says "I will put enmity between you and the woman, between your seed and her seed." This refers to Jesus (the "emnity") and Mary (the "woman"). The phrase "her seed" (spermatos) is not seen elsewhere in Scripture.
Gen 3:15 / Rev. 12:1 - the Scriptures begin and end with the woman battling satan. This points to the power of the woman with the seed and teaches us that Jesus and Mary are the new Adam and the new Eve.
John 2:4, 19:26 - Jesus calls Mary "woman" as she is called in Gen. 3:15. Just as Eve was the mother of the old creation, Mary is the mother of the new creation. This woman's seed will crush the serpent's skull.
Isaiah 7:14; Matt. 1:23 - a virgin (the Greek word used is "parthenos") will bear a Son named Emmanuel, which means "God is with us." John 1:14 - God in flesh dwelt among us. Mary is the Virgin Mother of God.
Matt. 2:11 - Luke emphasizes Jesus is with Mary His Mother, and the magi fall down before both of them, worshiping Jesus.
Luke 1:35 - the child will be called holy, the Son of God. Mary is the Mother of the Son of God, or the Mother of God (the "Theotokos").
Luke 1:28 - "Hail Mary, full of grace, the Lord is with you." These are the words spoken by God and delivered to us by the angel Gabriel (who is a messenger of God). Thus, when Catholics recite this verse while praying the Rosary, they are uttering the words of God.
Luke 1:28 - also, the phrase "full of grace" is translated from the Greek word "kecharitomene." This is a unique title given to Mary, and suggests a perfection of grace from a past event. Mary is not just "highly favored." She has been perfected in grace by God. "Full of grace" is only used to describe one other person - Jesus Christ in John 1:14.
Luke 1:38 - Mary's fiat is "let it be done to me according to thy word." Mary is the perfect model of faith in God, and is worthy of our veneration.
Luke 1:42 - "Blessed are you among women, and blessed is the fruit of your womb, Jesus." The phrase "blessed are you among women" really means "you are most blessed of all women." A circumlocution is used because there is no superlative in the Greek language. Note also that Elizabeth praises Mary first, and then Jesus. This is hyperdulia (but not latria which is worship owed to God alone). We too can go through Mary to praise Jesus. Finally, Catholics repeat these divinely inspired words of Elizabeth in the Rosary.
Luke 1:43 - Elizabeth's use of "Mother of my Lord" (in Hebrew, Elizabeth used "Adonai" which means Lord God) is the equivalent of "Holy Mary, Mother of God" which Catholics pray in the Rosary. The formula is simple: Jesus is a divine person, and this person is God. Mary is Jesus' Mother, so Mary is the mother of God (Mary is not just the Mother of Jesus' human nature - mothers are mothers of persons, not natures).
Luke 1:44 - Mary's voice causes John the Baptist to leap for joy in Elizabeth's womb. Luke is teaching us that Mary is our powerful intercessor.