Question

I very much want to study the Mekhilta, the Sifra, and the Sifrei, since in my understanding they illustrate the mode of thought of the Sages and their way of deriving laws from the verses.
How do you suggest approaching this study of the derashot?
As I understand it, most of the derashot are in the style of: “It could have written X, but instead it wrote Y to teach Z.”
I thought of studying in the following way: to read the verses, ask what the parameters of the commandment that emerge from them are, and ask whether there are repetitions or seemingly superfluous formulations in them (to what extent? I’m not sure…).
After that, to read the midrash and try to see the similarities and differences between my first reading and theirs, and to understand how they interpreted it (by the way—how much can one say that the derashot are based on the thirteen hermeneutical principles? Very often it is hard to assign a given derasha to one principle or another).
I am, however, aware of the gaps in this basic approach—various principles such as “A matter that could be derived by an a fortiori inference, Scripture nevertheless took the trouble to write explicitly,” “The Torah speaks in human language,” and so on. 
What do you think? Is there, in your opinion, a method that gets closer to the truth on this subject? Any reading recommendations? (I understood that you yourself have books or articles on the subject, but I was not told their names.)