How does the number of transcripts Christians have compare to some of the other ancient writings like those of Plato or Homer?

This is very interesting! The copies of other ancient manuscripts are often many hundreds of years later than the originals. Sir Fredric Kenyon, one of the greatest authorities in the field of New Testament textual criticism, adds: "Scholars are satisfied that they possess substantially the true text of the principle Greek and Roman writers whose works have come down to us of Sophocles, of Thucydides, or Cicero, or Virgil; yet our knowledge of their writings depends on a mere handful of manuscripts (in some of the Greek & Roman writings, we have only a few copies), whereas the manuscripts of the New Testament are counted by hundreds, and even thousands." The New Testament has 5,300 known Greek manuscripts available. It is a fair statement on the basis of the evidence that no crucial doctrine of the Christian faith is under any attack or discredited because of errors in copying or transmission. Therefore, the Bible is an accurate record of what Jesus said and did!