WOOO-HOOO!
Praise God form who all blessings flow!
Matthew, is writing to the Jewish side and starts at the birth of the Jewish people - Abraham. He is writing of the divinity of Jesus.
Luke, a doctor, starts where a doctor would, the beginning of mankind. His Gospel is focused on Jesus as a man. Also, Luke is referencing an oft-forgotten passage in the old testament that allows for inheritance through the female line.
Dr. Chuck Missler has a great article that describes the significance of each.