It is interesting that one can find some similarities between certain aspects of Christianity and other religions. I suspect that over time there has even been some sythesis of a few aspects of those other religions. But I hardly think that what has been put forth qualifies as parent/child religions. After all, there are also similarities with some Native American religions and that of Australian Aborigines. But only a fool would make the claim that there is some sort of connect on the basis of a few bits of parallelism. Besides, with religions such as the Mithraism, Gnosticism, or Emperor worship there is even more that stands in contrast than there is that is similar.
So, where does one turn to get a glimpse at the earliest form of Christianity? Simple answer, the book of Acts. The most primitive interpretation of the meaning of Jesus is found in the book of Acts with its account of the preaching of the early church -- preaching that is pre-Gospel writing; preaching that is largely pre-Pauline; preaching that records some of the earliest oral tradition of the infant church.
In that record we have a small group of Jewish disciples, convinced that their crucified master has indeed risen from the dead, who begin to declare his messiahship. This is not a pagan idea, this is an idea that has Jewish roots. There initial call is not to the Greek world at all, but to other Jews. They ask their fellow Jewish breathern to repent and turn in faith to Jesus, the one they had just crucified and recognize him to be Israel's long-promised messiah. In time it will break with Judaism as it sees the salvation promise as being available equally to Jews and non-Jews alike. When this happens, it quickly grows among the God-fearing Greeks who frequented Jewish synagogues.
Jewish-Christians at first press for the connection to Judaism to be kept, but under the leadership of Peter, Paul, and James and their testimony that God's grace is available to all without the need for non-Jews to convert to Judaism in order to receive it, Christianity takes off and enters the pagan world. There it will have to deal with new assaults to its self-idenity. Most of which I believe it passes, some it no doubt failed. But these are tangential issues compared to the questions of what was core and without a doubt the primitive kerygma of the Church has its focal point in the death and exaltation of Jesus the Messiah appointed to bring mankind salvation by God's gracious actions in allowing him to become the universal atoning offering of God's self for fallen and unreconciled humankind. But in the Christ that reconciliation takes place. This happens not just by the work of the cross, but also that as the Messiah Jesus will return to bring God's Kingdom to its eschatological consumation. (For example of that see Acts 3:19-21, long before Paul is preaching the cross.)
This Kingdom theme is Jesus central theme in his preaching and is among the themes of the earliest preaching of the church, prior to it leaving Jewish soil. Indeed, even after it has left Jewish soil for Hellenistic lands, carried their first by Barnabas and then joined by Paul, I find it of great interest that the summary which the book of Acts provides of Paul's preaching to the Gentiles is the utterly non-Hellenistic phrase, "the Kingdom of God" (Acts 14:22).
The other theme that we see in the most primitive kerygma of the Church is the proclamation that "Jesus is Lord." One might be tempted to see in this usage similar to the Roman usage of Lord as an expression of simple courtesy. But closer examination of how it is actually used reveals something completely different. The term "Lord" is not used indiscriminately in the speech of all sorts of persons, but is usually restricted to those appealing for supernatural help. (Source: The Self-Disclosure of Jesus, Geerhardus Vos, c. 1954, p. 129ff.) One of the best clues to the history of the word is in the Gospel of John, where the word "Lord" is used of Jesus only 3 times in the narrative portions of the first 19 chapters, but is used 9 times in the last two chapters which speak of Jesus as the risen Lord. Apparently, this evangelist feels it is appropriate to speak of Jesus as Lord after his resurrection, but does not feel the designation is so appropriate in Jesus' earlier ministry. This suggests that the title "Lord" is not just a courtesy extended to a teacher, but "belongs primarily to Jesus as the Risen and Ascended One" (The Names Of Jesus, V. Taylor, Macmillan, c.1953, p.43). But the even more impressive fact is that the term "Lord" is used both for God and the exalted Jesus. For instance, in Acts 3:19 it is clearly used for God and this usage can be traced back to the Septuagint where kyrios, (the Greek word which we translate as "Lord" in English) is the Greek translation not only of the Hebrew word Adonai but also of the Hebrew's covenant name for God, Yahweh. Because "Lord" is used this way to refer to the one God of Israel, it is all the more amazing to find the term used of both Jesus and God as the same time. For in doing so, even the earliest church, composed entirely of Jewish disciples of Christ, long before Paul is ever on the scene, are Jesus one with God. So much is this the case, but the term is used by the early church "of both God and the exalted Jesus in practically interchangeable contexts" (A Theology of the New Testament, George Eldon Ladd, Eerdmanns Publishing, c. 1974, p. 339). Most certainly, Paul will expand on this idea, and Greek and Roman culture will have parallels for it with their pagan cults, but it began with and is therefore derived from this small group of Jewish disciples led by Peter.