I think there is a bit of a misconception here. I'll start with a few problems with the questions and end with a few suggestions.
First, StackExchange doesn't do well with open-ended and opinion-based questions. You might find other fora a better option for the question as you actually asked it. It might even make for a decent discussion in the chatroom.
Second, it's not really accurate to say you want to apply a "school of thought" to a text. A theory can be used to provide a lens, and a school of thought is the intellectual context in which that theory is developed. Saying you want to apply a school of thought to a text is a quick shorthand way of saying you want to apply a lens. So that's what you ought to be talking about, if I understand your question correctly.
In that case, you have options, like reading it through a feminist, Marxist, post-colonial lens. You could also read it in light of contextualist, structuralist, post-structuralist, postmodern, historicist, post-historical, etc. theories of literature. All these approaches are created in order to better understand the text.
The issue is that the breadth is so vast. It would be like an alien saying: "I want to study earth. What science is best used to study it?" Each reading will yield different results, and some will be more relevant than others, certainly. But then the applications will also be just as varied. At any rate, you can't get to it all and have it make sense.
Even for a single text like Great Expectations, you have many volumes of scholarship dedicated to understanding it.
The best thing to do is to get a companion to the text, like those put out by Cambridge (whose series are really useful for students, imo!), Oxford, or Routledge that have essays covering some of the basics of the work in question. Usually these edited volumes cover enough of the approaches for you to get an idea of current scholarship and how it works.