The Jewish Churches which accepted Christ. Jesus was a Jew as well as His disciples. As far as "with a non-contradictory body of teaching and an unbroken line of Apostolic and Petrine successors", I'm not sure what that means (it's certainly not a Biblical concept) but when you show me 12 Catholics going out in the world (from town to town) healing the sick, restoring sight to the blind and bringing the dead back to life we'll reopen this discussion.
If Christ COMMANDS us to take our disputes “to the church,” the Church must speak for Him, must’t it? It must teach Truth, and It must do so infallibility.
Since Jesus is Truth Itself, it is IMPOSSIBLE for Him to COMMAND us to take our disputes to an ERRONEOUS Church.
Now, when we look for an infallible, visible Church, in existence from Apostolic times, then AT THE VERY LEAST, the teaching of this Church must be non-contradictory.
Regarding Apostolic succession, see Acts, where Judas’ OFFICE, or bishopric (KJV), is filled by Matthias. The Apostles appoint their successors. And this line of successors exists unbroken, until today, in the Catholic Church (and the Orthodox Churches).
Peter’s office as leader of the Apostles, he who holds the key of the eternal Davidic Kingdom (Isaiah 22:22, Matthew 16:19, Revelation 3:7), exists today in the papacy.
Regarding Apostolic miracles, the bishops are not Apostles, because Apostles walked with Jesus. They are the successors to the Apostles. But there are certainly miraculous healings within the Church to this day. I have personally met two people cured of terminal cancer through the ministry of a priest, given the gift of healing, Fr. Aniello Salicone. He has laid hands on me, and I was overwhelmed with a sense of peace which I had never experienced before.
Send him an email. He answers every one.
http://www.catholicseniors.com/aniello.html
If you’re looking for documented, miraculous healings, do some research on Lourdes.