Thank you for the book recommendations, I'll look for those on amazon.
The reason I asked this is because I was reading this book https://www.amazon.com/gp/product/0300115970/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0300115970&linkCode=as2&tag=httpwwwchanco-20
In it the author writes that the early church of Rome was most likely ruled by a council of elders and not by single ruling bishop. There is no proof that Linus, Clement, etc. were actually Popes. A single bishop a Rome didn't occur until later in the 2nd century he claims.
The first century was incredibly turbulent.
Much was destroyed. The letter of Clement seems to suggest
Roman supremacy over the other churches, despite the fact
that the church in Rome was the most persecuted most of
the time, with the only possible exception being in Jerusalem.
This is a complex subject. Irenaeus and Tertullian are among
the most important sources. Linus appears in Acts.
The apostle John, Polycarp line was in Smyrna.
Don't confuse all the churches with apostolic succession with
the bishop of Rome as the primacy among them. It is natural
that the powers and abillities of the Roman bishops increased
when the persecution of Christians in Rome was made illegal
by Constantine.
I think your best bet is the Charles Coulombe book above.
If you want a sense of the confusion which Christianity
sowed among the heathen get a copy of Patrology
by Johannes Quasten.