I think, Jack summed it up perfectly in his response. So, just a few remarks.

First, I would completely disregard Constantine. When you look at writings of Irenaeus from Lyon (born in Smyrna, apparently into a Christian family), particularly his Against Heresies, you will see that the Christian canon was in 2nd century AD already in roughly the shape as we know it today. Irenaeus writes about Gospel as “handed down to us in the Scriptures, to be the ground and pillar of our faith.” He then identifies the pillars of faith as Matthew, Peter, Paul, Mark, Luke, and John. You will also find mentions of Book of Revelation in his work.

Second, although I agree that Saul was an overzealous fundamentalist who is responsible for the most of the confusion, I would say that his rendering of Jesus is not so much Mithraic as it is Pharisaic. The reason why Saul's Jesus appears Mithraic is that, at the time of Jesus, Judaism was basically henotheism indistinguishable from other pagan cults of the era (for a current example, and for all practical purposes, look no further than Santana Dharma aka Hinduism). Thus, incorporating a messianic figure into the framework would yield a “god” akin to Mithra, but also Osiris or Dumuzid, etc

Third. Looking at fragments of historical developments it becomes clear that it was Christian bishops who sought political influence. Most probably to legitimize their sect and stop persecution (which was not that severe as it is portrayed, but even one dead is one too many). Hence, even in time when there were several major centers of Christianity and no Roman Catholic Church to speak of, Irenaeus refers to the Church of Rome as one with “superior origin”, with which”all the churches must agree”.

Fourth, and IIRC, Keith considers even Gospels influenced by Saul, thus unreliable. I for one disagree with that, but only because Jesus in Synoptics and John (which can withstand cross-referencing with Gnostic Gospel of Thomas) is quite different from the one in Saul's epistles. Despite the fact that Gospels where, indeed, either edited or composed from other sources with added fables to reflect Saulian theology (e.g. original Mark ends with several women visiting an empty tomb meeting a mysterious guy in white, but no explicit resurrection). Simply speaking, the character of Jesus in Gospels has a different flavor to the one hinted at by Saul. And one can make an educated guess about how the sources quoted (written or perhaps only oral) looked like.

However, I have to admit, the gaps in the final image are still huge. But, when you consider Jesus as consummation and peak of Judaism (similarly to Siddhartha and Hinduism) it's not that hard to see a pretty plastic picture of a genuinely enlightened teacher in the context of Hebrew world within the confines of Roman empire. And from that, one can “rebuild” Jesus' message.