They did have the "old testament" and there's also pretty strong evidence that the books of the new testament were in common use long before the 2nd century. Paul's letters for example were surely being passed around between churches.
True - they did have the Septuagint (which included the Deuterocanonical letters) - but not all the books were accepted by all.
Your next statements are also correct -- that MOST of Paul's letters were widely in circulation. There is the notable exception of the letter to the Hebrews that was disputed.
And Revelation was strongly disputed well into the 2nd century.
However my point was that we can't call the first century Christians as "Biblical Christians" as they didn't define the canon and it varied. What they did call themselves was "followers of the way" and they held to the Gospel and what they were taught by designated teachers/bishops/overseers
This is why Paul says "some say they are from Apollo, some from Paul, some from Cephas etc." - meaning if you had two followers of the way disputing then they would try to prove their antecedents from where they learnt/were taught.