I'm not sure I would wholly agree with the above - while it is true you should avoid just reading the same tick box list as every other candidate, which doesn't give them much to go on, I wouldn't suggest just looking for "obscure" texts. If you read something unusual, and your interviewer is actually the leading expert on that, but you didn't really "get it" that much due to the obscurity of it, you're just going to make yourself look foolish.
Read the things you're actually interested in, and then read texts that support that - criticisms and essays on the text/it's author contemporary to it's release, as well as more modern ones, texts that predated it from which it referenced or drew upon in some way. For example, it's entirely reasonable to read and want to comment on say, Beowulf. It's not that obscure a text (I believe many schools teach it in primary and secondary school) but it is a major work that still has research and criticism written about it today. However, you should look deeper - considering nuances in the "translation" of it from old English to modern English, cultural aspects of Anglo-Saxon life and diplomatic relations at the time as evidenced by historical and archaeological analysis outside of the literary sphere. Similarly for Shakespeare, considering different folios and quartos and in general whether the plays remain representative of their original form through these, etc.
Once again, the context (historical and cultural) is also important, and you can do a lot of wider reading in this regard; Literature is not just reading (fiction) texts alone. You can also look more broadly at different forms of text, for example the historical development of the concept of the novel (and cultural issues e.g. whether the debate of The Tale of Genji as a novel vs other form stems from Orientalist biases, while Don Quixote is readily accepted as representative or establishment of the form, and is a European text published during a period of Spanish dominance in Europe) or the nature of the form of the novella.
The key thing is to know what you've read well, which extends beyond what the singular text itself contains - looking into the contextual writings around it. You probably don't want to pigeonhole yourself into only one text/style/genre/era/etc now, but you can certainly just consider a handful in great detail. Quality over quantity. Bear in mind as well that words have specific meaning in the field - things like "ideology", "discourse", and "postmodern(ism)" for example follow specifically from particular critics/philosophers works, so make sure you understand what these mean and don't just use them willy-nilly without understanding them (and avoid it otherwise). In general, looking into major literary critics (like Foucault) might be quite useful wider reading rather than simply reading more "literary texts".