You should grab the compilation of his original papers, they're generally readable. He was sort of guessing, but he did have a general line of thought he was going through. He actually wrote down the time-independent equation first, and didn't write down the time-dependent one until the fourth paper. And in his fourth paper, he writes it down as a second-derivative equation (the square of what we call the Schrödinger equation) and argues that the imaginary parts are mathematical and not physical. In other words, it took some tries to get to the modern understanding.
He also did not like Born's interpretation which we now take to be correct.