Both sound interesting, so how about both?
Well the reason why I claim it isn't man-made but GOD-made is because Christ founded one Church (Matthew 16:19). We recognize that the Church isn't THE authority -- that would be God, but that God has given His people a Church to author His authority through the Holy Spirit (John 20:21-22). We recognize that the Bible His written Word, and remarkably, it was the Catholic Church that compiled and canonized this book which we call The Bible. And it was through the Holy Spirit's ability to speak through those bishops in the close of the 4th century that we believe in the Bible to be God-breathed.
The Early Church fathers--these were the students under some of the Apostles--spoke explicitly of one Catholic Church (this term was recorded at least as early as 110 AD by Ignatius of Antioch--a student under John). They wrote about Church direction, demanding the scriptures (even before its canonization) be respected and used in teaching and not changed in teaching. They wrote about the role of the clergy and the laity, but more importantly, the invisible Church -- the spirit of it which God left for us.
It has respected Christ's teaching for 2000 years and has practiced it since then. Most people think the Catholic Church is the clergy and maybe the laity, but that's only the body of the Church -- the Church, like man, has a soul if you will.
As for denomination, this is trickier because on one hand, Catholics don't mind responding when asked "what denomination are you" with being Catholic. We do this because the Church believes Protestants are also Christians. The Catholic Church believes Presbyterians, Baptists, Non-Denominational, Anglican, Methodist, Pentecostal, etc. etc. to be Christians so long as they believe in God the father, the death and resurrection of His only son Jesus who was conceived of the Holy Spirit and born of a virgin, the forgiveness of sins, eternal life in Heaven, the free gift of grace, and the worship of only one--that being God.
That said, because Catholicism also teaches that there is only one Church, it doesn't promote the notion of mulch-denominations. Do Catholics believe non-Catholic Christians can reach heaven? Absolutely. Do Catholics believe in working with other denominations in pursuit of spreading the Gospel? Absolutely. Do Catholics regard Protestants who are sincere in the Christian faith as Christians? Absolutely! But do Catholics support division? No--the goal is to bring all to the fullness of the body of Christ. Catholics regard Protestants as our fellow brothers and sisters in Christ, albeit separated from us.
And as for the subject of baptism, Catholics credit non-Catholic baptisms as valid baptisms so long as they are in the Tridentine formula (ie, done in the name of the Father, the Son, and the Holy Spirit).
