I have written a Christmas post on Matthew and Luke, so these are further reflections on their work.
Matthew– (I also have a post on the three list of fourteen names in Matthew.) Scholars have said that Matthew’s genealogy is Joseph’s family tree, in part because it includes Solomon. But it makes since because the focus is really on Joseph and his dreams/part of the story. However, the probable source still was Mary! She was the only eyewitness to these events.
Mark– Mark/Peter are the only writers who do not include a narrative about Jesus’ birth or linage. I believe that Mark witnessed much of the ministry of Jesus (I think he was the boy who supplied the fish and bread for the feeding of the five thousand and lost his clothes in the Garden.) If Mark was the first Gospel written I could understand why it was started with John the Baptist, they got right to the ministry. But to not down play the book Mark does confirm John the Baptist’s story and that Jesus “came from Nazareth”.
Luke– The focus person in Luke’s Christmas story is Mary and her part of the tale. So, it makes sense that the genealogy in 3:21 is Mary’s. Her line comes through Nathan (also a child of “Uriah’s wife”). Luke should also be the source for the year we chose for Jesus’ birth. The two timestamps here are 2:1 (Caesar Augustus) and 3:1 (15thyear of Tiberius). Augustus ruled until 14 A.D., he also helped the spread of the Gospel by continuing the building of the Roman road system.
John– he also tells the Christmas story but from a different point of view. Jesus’s genealogy is the most important one; it has God and Jesus the Word and Light. John also talks about John the Baptist just like the other three Gospels. 1:4 is a different take on the Star and the angels. In between all of this comes accomplishments that Jesus and John did before the symbolic baptism/parting of the Red Sea.