I believe the gospels. What you're pointing out aren't contradictions. An angel told Mary she was going to become pregnant by the Holy Spirit and give birth to Jesus. After she became pregnant an angel talked to Joseph in a dream and told him not to worry about Mary being pregnant.

The gospels don't contradict. You could have an account where one group of people is mentioned. Another account could mention other people. They both can be true.

Even if there are contradictions, you always have contradictions in eyewitness testimony. I would be more concerned if all accounts agreed on every single aspect.

The Gospels were written by Matthew, Mark, Luke, and John. They were written by eyewitnesses and those who talked to eyewitnesses. Mark appears to be the earliest synoptic gospel. It would appear that Matthew and Luke used Mark as a starting point.

I've studied the gospels more than almost anyone who didn't go to a seminary. I put together a chronological account from all four gospels into a single document. It's amazing how they reinforce each other. Such as:

(Matthew 9:20-21 NIV) Just then a woman who had been subject to bleeding for twelve years came up behind him and touched the edge of his cloak. {21} She said to herself, "If I only touch his cloak, I will be healed."

(Mark 5:25-32 NIV) And a woman was there who had been subject to bleeding for twelve years. {26} She had suffered a great deal under the care of many doctors and had spent all she had, yet instead of getting better she grew worse. {27} When she heard about Jesus, she came up behind him in the crowd and touched his cloak, {28} because she thought, "If I just touch his clothes, I will be healed." {29} Immediately her bleeding stopped and she felt in her body that she was freed from her suffering. {30} At once Jesus realized that power had gone out from him. He turned around in the crowd and asked, "Who touched my clothes?" {31} "You see the people crowding against you," his disciples answered, "and yet you can ask, 'Who touched me?'" {32} But Jesus kept looking around to see who had done it.

(Luke 8:43-48 NIV) And a woman was there who had been subject to bleeding for twelve years, but no one could heal her. {44} She came up behind him and touched the edge of his cloak, and immediately her bleeding stopped. {45} "Who touched me?" Jesus asked. When they all denied it, Peter said, "Master, the people are crowding and pressing against you." {46} But Jesus said, "Someone touched me; I know that power has gone out from me." {47} Then the woman, seeing that she could not go unnoticed, came trembling and fell at his feet. In the presence of all the people, she told why she had touched him and how she had been instantly healed. {48} Then he said to her, "Daughter, your faith has healed you. Go in peace."