Based on this description, KJV should be pretty accurate then. You wouldn't have needed the original texts by the apostles.
You're saying vast amounts of people copied the apostles' texts at the time. Any mistakes made would have been like typos if the majority of people copying it were doing so honestly.
After that, King James of England ordered that the Bible be translated into English by a group of collaborating scholars who had gathered as many versions of the text as possible.
Whether stuff in the Bible is true is a whole other question. I'm not a Christian myself but it seems to me like they would have ended up with quite an accurate text for English speakers.