In order to tell something about the New Testament church, you have to read the NT.
See post 10785
As you've well-noted, there is nothing in Scripture about any apostolic succession. There is only apostolic teaching, passed down through Scripture.
The snippets of quotes Rome pushes forward as some kind of evidence shows just how desperate Rome is to substantiate its error. They take a line here and there from some translation of something and cobble it together to say the pope and his magisterium are infallible in matters of faith and religion when Scripture teaches only Christ is infallible and His teachings are what men are to follow. Teachings found in the Bible, open to all.
Yes, you have to read the New Testament — which is what is done each day in Church at mass. And, unlike some of your groupings, we read the NT, OT in their entirety — we read the Gospels, the Epistles, Revelation, we read psalms, the Pentateuch etc. all in mass —> we, Christ’s Church, the One Holy Apostolic Catholic Church ARE the New Testament Church. This is evidenced in the reading of Acts, in the writings of First Century Christians (Didache, +Ireneus etc).