It may be worthwhile when reading any famous work to read it from the perspective of a commentator who will act as a guide. That is because these works may be very easy to read, but difficult to understand or situate within a broader context. This commentator becomes the window through which one understands the work by providing the "background" the OP desires.
If that is the case, the question is which commentator to use as a guide to Wittgenstein's Tractatus? There are many people who have written about the book. The one I recommend is G. E. M. Anscombe's An Introduction to Wittgenstein's Tractatus: Themes in the Philosophy of Wittgenstein.
Julia Driver summarizes her professional life:
Gertrude Elizabeth Margaret Anscombe was one of the most gifted philosophers of the twentieth century. Her work continues to strongly influence philosophers working in action theory and moral philosophy. Like the work of her friend Ludwig Wittgenstein, Anscombe’s work is marked by a keen analytic sensibility.
So, Anscombe is a philosopher worth knowing in her own right and she was closely associated with Wittgenstein.
Driver discusses their relationship further:
Anscombe met Wittgenstein at Cambridge, after her graduation from Oxford. She attended his lectures and became one of his most devoted students. She believed that it was Wittgenstein’s lectures, for example, that freed her from the trap of phenomenalism (MPM, ix). When she returned to Oxford she continued to travel to Cambridge to study with Wittgenstein.
Anscombe also became one of Wittgenstein’s good friends and then, after his death in 1951, one of the executors of his literary work. Ray Monk wrote that Anscombe was “…one of Wittgenstein’s closest friends and one of his most trusted students, an exception to his general dislike of academic women and especially of female philosophers. She became, in fact, an honorary male, addressed by him affectionately as ‘old man’.” (Monk 1991, 498).
Anscombe translated Wittgenstein’s Philosophical Investigations (1953), and wrote an introduction to the Tractatus in 1959 (the work had originally been published in 1921). She organized major publications of Wittgenstein’s later work in, for example, Remarks on Color and Zettel. She also translated a number of his other works.
The Monk reference is to his biography, Ludwig Wittgenstein: The Duty of Genius.
Someone this closely involved with Wittgenstein may be a worthy guide to understanding him better.
Here is the question:
How much background do I need to read this book? And, in such case of needing background at all What background should I expose myself to, in an effort to properly understand and interpret this book?
Anscombe's introduction may be all the background one needs for an initial reading of the Tractatus. Both of these works can be read (and re-read) together. After that initial understanding one will be in a better position, that is, one will be able to trust one's own judgement better, to look for other sources or explore other themes related to either of these two philosophers.
Anscombe, G. E. M. An introduction to Wittgenstein's Tractatus. (1971)
Driver, Julia, "Gertrude Elizabeth Margaret Anscombe", The Stanford Encyclopedia of Philosophy (Spring 2018 Edition), Edward N. Zalta (ed.), URL = https://plato.stanford.edu/archives/spr2018/entries/anscombe/.