Above all, what did Author Miller want to capture in writing The Crucible?

The primary message that author Arthur Miller was trying to convey in The Crucible is that hysteria and fear come at a high cost. This story draws a parallel between the witch trials that occurred in Salem, Massachusetts and the communist witch hunts of the Red Scare in the author's time.
The hysteria featured in The Crucible begins with a series of accusations by the local minister's young niece, Abigail. The town becomes paranoid of spectral threats to their homes and livelihoods, resulting in real violence towards innocent people. In this sense, Miller is trying to convey the importance of making decisions based on evidence rather than superstition and hearsay. What begins as a seemingly innocuous rumor can turn into a flame that engulfs an entire community. Social pressure is another major theme as many of those who accused the "witches" in the story were just going along with what others told them. Others were afraid that if they did not jump on the bandwagon of accusing their neighbors of being witches, they themselves would become the targets of the mob's ire.
To summarize, Miller wanted to capture the idea that the same paranoia and violence that resulted in the New England witch trials have the potential to lead to more violence in all generations. While the target of the hysteria changes, the human suspicion and weaknesses underlying it remain the same and we are all vulnerable to them if we do not temper them with reason.