I'm not sure that I agree with the idea that the Jewish conception of G-d is closer to the Christian idea than it is to the Muslim idea. I think that, while all three religions share some common ideas about G-d, each is pretty distinctive. For instance, the Christian belief in a divine Trinity is utterly antithetical to the Jewish and Islamic belief in a wholly incorporeal G-d. Both Judaism and Islam forbid graphic representations of G-d as a result; Christian art, of course, is dominated by representations of one or more parts of the Trinity.
As a Jew, I'd agree with you that Christianity evolved out of Judaism -- with the caveats that I'd say (1) it evolved out of a totally different form of Judaism to what is practised today, a version that centred around priests, sacrifices and the Temple(s). Rabbinic Judaism was also formed in the early centuries of the Common Era (eg after Jesus's death), and (2) it evolved so much that it is very dramatically different in terms of theology, ritual, practice and observance.
Star Traveler asserts that Judaism and Christianity are both Abrahamic religions and that Islam is not -- but elaborates a theological position, rather than a description. Jews more than just the divinity of the Messiah, they reject most of the fundamental tenets of Christianity -- original sin, for instance.
But broadly speaking, Christianity and Judaism seek to serve the same God, do they not? And is not their God the God of Abraham, Isaac, Moses, and Elijah? And don't they share, generally, much of the Old Testament as sacred scripture?
From what I have seen of the Koran, it is radically different from the Old and New Testaments.
Messianic Jews, who are a growing group and are like the First Church in Jerusalem (of whom we hear from James [Jesus' brother] and Peter) are evidence of the tight integration of Jews and Jesus Christ. You don't find such a thing as "Messianic Muslims" (either in history or the current day).
There is no connection between Islam and Christianity. But Jews and Christians have the same God as Abraham, Isaac and Jacob -- who is the One true God ("Allah" being one of the many false gods that the God of Abraham, Isaac and Jacob stands against).