Superconductivity: Bogoliubov vs Spin Analog vs Variational vs ? Methods

I have been studying the BCS theory of superconductivity recently. I have three solid state texts that approach the Reduced Hamiltonian in three different ways:

Ziman, Principles of the Theory of Solids, outlines the method of Bogoliubov,

Kittel, Quantum Theory of Solids, details the Spin Analog method of Anderson (he also reviews the Equation of Motion method, which, at first glance appears to be the same as the Bogoliubov method), and

Harrison, Solid State Theory, uses the BCS Variational method.

These are all obviously old texts. I think it is interesting that there are multiple ways to approach solving this problem, but I also would like to prioritize my study. So, I have two questions:

1. Over time has one method (maybe not even one of these) become the more preferred method to teach the solution of the Reduced Hamiltonian?

2. Are there particular advantages to learning one method over the others? For example, the Bogoliubov method appears to be useful studying superfluid He. The variational method appears to be a straightforward extension of what is taught in elementary QM, thus it may be the easiest as an entry level solution.

I appreciate any thoughts on this!