The texts you see in the Bible don't stand a critical inspection. They weren't written when Jesus was alive, but a lot later. The first ones have some credibility as there were still some old people alive who had been children when Jesus was alive, but even that doesn't necessarily mean that they're automatically true. A story becomes a myth, a myth becomes a legend and so on. One of the basics of historical research methods are thinking about motives of the author. If a king writes about his conquest he'll probably lie to make himself look better. For instance there are Viking texts that say that they attacked Konstantinople with...ummm... was it 800 ships. And that is not to be taken seriously as such an attack would've left like half a Sweden deserted. So particularly the miracles you read in the Bible should sound an alarm. Is there a reason Jesus should be made look as good as possible? Hell yeah.
You have to remember though that the Jewish culture before, at the time of Jesus and after was an oral culture. There were people that had the job of remembering exactly what a person said and they would retell exactly what they said later. Through the years the stories would not change because people knew the story and if the storyteller changed the story the people would know. The Gospels were written as early as the 60's and as late as the mid 80's if I remember correctly. So it was only 30 years after Jesus' death and resurrection that they wrote the Gospels. The reason they waited so long to write it down was because they thought that Jesus would come back during their life time. When people started dying off they realized that they needed to write down what they experienced and what Jesus said so future generations could know of Jesus.
To address the miracles of Jesus. You said that should sound an alarm. For a scientifically educated person as you are and we all are, it would sound an alarm. But at the time of Jesus they did not have the field of science as we know today. It was a pre-scientific world. And these miracles were not just preformed in front of the lower uneducated class. Jesus preformed miracles in front of the Jewish religious leaders and the educated people that were skeptical. And they believed he had preformed miracles because they accused him of breaking the Sabbath by healing a man. The Pharisees (a Jewish religious sect) had added hundreds of rules and regulations to the original 10 commandments that Moses was given for the Israelite people. It is hard for us to imagine miracles because we don't see people healed from lifetime sickness and crippled ness. But if Jesus was who he said he was (God incarnate) then why couldn't Jesus do something that everybody else couldn't
In an earlier post somebody mentioned that the Gospels were different and the stories came in a different order so there for they couldn't be reliable. If you talk to a police officer about investigating a crash they will tell you that everybody has a different story of what happened. It's because they were at different angles and had a different perspective. But they all describe the same accident. If the Gospels would have said the same exact thing then it is time to worry about some funny business.
You are right about kings wanting their missions to look well. It is a part of critical analysis of any text, looking at motive.