Here's a quick summary.
Jesus Christ Established a Visible Church On Earth
Basically, it is the hermeneutic of continuity. There is one plan of salvation that started when the Father cursed the serpent in the Garden and made a promise that Eve's seed would be in enmity with the serpent's seed. Slowly, throughout history God revealed Himself to humanity through the chosen people, little by little, until finally, in the fullness of time, the definitive revelation, the Incarnation of the Second Person of the Blessed Trinity was accomplished. There is no "break" between the age of nature and the age of law, and there is no "break" between the age of law and the age of grace. And there is no "break" nor will there be, until the parousia. Through it all, there is a visible, organized, God-led, peopled, institution through which God interacts with his people. First it was just a couple (Adam and Eve), then it was a family (Noah), then it was a tribe(Judges), then it was a nation(Saul), then it was a family of nations (David, Solomon), now it is the world-wide Church. Is there sin in the Church? Of course! Just is there was sin in every institution throughout salvation history but that doesn't negate the fact that it is the instrument through which God acts to save His people. Do all the institutions look the same throughout all the centuries? Of course not! There is development just as with everything else. But Jesus promised to build His Church and to stay with her (His bride) until the consummation of the age. Don't leave Peter because of Judas.
Why did God have to become human flesh? What was the purpose? He could have redeemed us any way He wanted to. Why did He choose this way? Because he created us as flesh and spirit. He knows we live in the flesh, we learn and grow in the material world. So he became man. Throughout history God has always used matter to communicate with us, water, blood, fire, smoke, rocks, hills, animals, trees. Now is no different. He did not become man to found an invisible church. No, he uses matter because we are matter. Visible. Full of signs (sacraments). Led by real living people, not by words on a page.
Why did Jesus live? We know why He died, but what did He live for? What was the mission of His life? If his only purpose was to die, why didn't he just let Herod get him in Bethlehem? Or why not let the people stone him when they wanted to? He kept slipping away and telling folks that he healed not to tell anyone. Why? What was so important that he had to do before he died? The answer lies in the the first time that Jesus prophesied the manner of His death and that He would rise again. Check Matthew 16. Right after Jesus changes Simon's name to Rock (name changes are important, remember), then he is ready to go to Jerusalem one last time. Verse 21: From that time Jesus began to show his disciples that he must go to Jerusalem and suffer many things from the elders and chief priests and scribes, and be killed, and on the third day be raised. So the purpose of Jesus' life was to found the Church under his kingship and give her the leadership model for them to follow while He is gone.
Whenever Jesus talks about his kingdom, he is referring to the Church which he is building on the pattern and as a continuation of the Davidic kingdom. Otherwise the prophecies about David's everlasting progeny would be false. Following the Davidic kingdom model, Peter is not the king. Jesus is. Peter is the prime minister. (Apostles are ministers with the power of binding and loosing, Peter is prime minister with the keys) If you read Isaiah 22 you see a great example of a prime minister in the Davidic kingdom. Shebna was thrusted from his office and Eliakim received the keys. He acts with the authority of the King. He opens and none shall shut, he shuts and none shall open. But he is not the king. Jesus, in the line of David, remains king. He appointed Peter and his successors to steward His kingdom until He comes again. (Also, btw, another good example of the Davidic kingdom model being followed in Jesus' kingdom is the queen mother. But that is another thread.)