Ultimately, I think the most fundamental question is this: What kind of subjects would you primarily be interested in? Someone interested in history is going to seek out a very different set of books than someone interested in philosophy or literature. Similarly, a biologist will have very different interests than an astrophysicist.
However, even here, I think this idea of an infinite library (as imagined by Borges) is actually more fiendishly complex than it might originally seem. Consider, for example, the case of classical literature and the wide array of ancient texts that have been lost over time. I can imagine that a classics scholar would be gleeful at the thought of finding long-lost works by dramatists such as Aeschylus and Sophocles or philosophers such as Aristotle. Here, however, the question must be asked: If there is truly an infinite number of works, not all of these lost texts will actually be genuine, and who is to say which texts were actually written by the authors in question, and which ones are nothing more than inventions of the library's infinite nature?
At the same time, there are other, even more abstract topics that might hypothetically be available for study: perhaps you might uncover a treatise providing an irrefutable explanation of the meaning of life, for example, or a flawless proof or disproof of God. (And how would you make sense of the very real probability of there existing both a flawless proof and a flawless disproof simultaneously with one another?) You might find histories of futures that have not yet come to pass. In practice, the possibilities are endless.