It may be true that the earliest memories of him reflect most closely who he actually was, but there is no guarantee that these early memories are not already information refracted or distorted or wrongly attributed to him. Why? Even setting aside the fact that the first Christians were charismatics who believed that Jesus continued to live and teach in their presence in some kind of spirit manner (a fact which made it fairly simple to attribute to the historical Jesus things said in his name by early Christian prophets), we can expect that even the first memories of him are already in the process of shifting because of the natural processes of human memory and also social memory formation. In other words, the way we remember is a function of our brains and our societies. It is now and it was then.
So my approach to the historical Jesus comes at the issue from a slightly different angle and with a slightly different goal than the questers that have gone before. Not that the historical Jesus has ever been a goal of my research, but nonetheless I have had to work out a solution to the problem myself in order to be able to understand the beginnings of Christianity. I would call my approach "Constructing Jesus." I would frame it as an attempt to come to understand the earliest memories of Jesus from all the sources available to us. I would work the sources in a way that I would lay out how the various communities constructed Jesus. I would then compare these constructions to see where there are intersections of early material that is being rewritten or reformatted by the early Christians because it is no longer useful or relevant to them in their present situation. And I would see what I had in its entirety. And I would not kid myself that I was looking at Jesus himself, but only the earliest memories of him that the communities constructed. For me, that would be good enough.
The main criterion for identifying the threads of this early material would be what I call simply "Theological Reinterpretation." That is, I would identify all the areas in the sources where the early Christians are clearly rewriting Jesus, where secondary development of him is certain. One example must suffice for now.
Mark 9:1 - "And Jesus said to them, 'Truly I say to you, there are some standing here who will not die until they see that the Kingdom of God has come in power."
This saying of Jesus appears to have a life of discomfort among the synoptic writers. Mark appears not to like its implication - that there have been followers of Jesus that have died and yet the Kingdom of God had not yet come in some eschatological manner. So he does something interesting. He places the saying sequentially right before the transfiguration story, which he hopes his reader will understand to be the moment that God's Kingdom manifested in power (rather than at the end of time). I would further suggest, based on other evidence that is too involved to post here, that when Mark did this he also recast an earlier source of his which had a version of this story (without the disciples) immediately following Jesus' baptism.
That this saying continued to cause distress and require further rewriting is evident from Matthew's treatment, who has softened the blow of a failed eschaton by reframing Mark's version to read: "Truly I say to you, there are some standing here who will not die before they see the Son of Man coming in his Kingdom." Then follows the transfiguration story which shows Jesus transformed as God's "son." Neat. No more cognitive dissonance here.
Luke too is highly concerned about what he has received from Mark. So he makes his own adjustments: "But truly I say to you, there are some standing here who will not die before they see the Kingdom of God." The End is no more, because according to Luke the Kingdom of God is already here among us (Luke 17:21).
Even more interesting to me is how this saying is still problematic to Christians today, so bible translators usually try to soften things by translating very woodenly "will not die" with "will not taste death". Now this is remarkable to me because usually bible translators try not to translate woodenly, but to convert the original language idiom into proper sentiment. When our ancient authors write "will not taste death" they do not mean that a person will flirt with death (and might not die), but that they will be dead. It is an idiom for "to die."
At any rate, this sort of analysis, done on a much more detailed level, would yield a good amount of information that I would label "earliest memories of Jesus." And one of them would be (based on a number of these sorts of examples) that the earliest Christian memories of him were of a Jewish apocalyptic preacher who taught that the Kingdom of God was in the process of being established on earth as part of the coming of the End of the world. The last part of this sentence is important because we must be fair to our sources who are all rewriting the saying about the Kingdom of God, because they think that, as it stood, it was a failed prophecy of Jesus. And they were trying to correct or reinterpret this failure in a new theological direction, which they did admirably. This means that the earlier memory they are rewriting is one that understood Jesus' message about the Kingdom of God in terms of an imminent End.
I didn't say you would like it. But as an historian one has to be willing to recover that which might not be "likeable," and leave it for what it is.