+1 for needing a clearly defined goal. For example, another question that needs to be answered: define "book". That isn't to be a smartass, but to ask an honest question. Are we limiting the definition to a clearly defined, cover-to-cover tangible tome? If not, would e-books on a solid state drive be just as valid?
The reason I ask is because it would theoretically be possible to put an entire encyclopedia or something as a singular reference file, and call it one book. Maybe it's a bit pedantic, but having a solid frame of understanding what your limits, restrictions, and goals are allow us to narrow down what is and is not truly vital for this project.
Lastly, to me this seems a nigh-impossible project without further defining the "sum of human knowledge". Even if we eliminate "superfluous" things like cultural works (specific songs and works of literature), or religious, mostly non-philosophical works (I'd argue that the Quran and the Bible would both need to be tossed, as both are far more focused on stories and parables to illustrate a way of life and religious belief than philosophy), there's still a TON of hard "knowledge" that transcends culture.
Biology for example, has so many specific daughter disciplines I doubt you could encapsulate it in the 150 itself, let alone a subset of the whole. There's vast sums of knowledge of animals, plants, the way the environment works, the nature of biochemistry and evolution, germ theory and more. Sure, you could get some basic books to cover the broad strokes, but that leads me back to defining the sum of knowledge: are we literally trying to preserve all we know, or just preserve enough to give someone the gist of what we've learned thus far. The former is a strict definition (as it means the sum of knowledge is literally the addition of every disparate part until we reach the total), while the latter is not and thus needs more definition as well. How much knowledge on a given subject or category is enough to be "enough"?
I actually worked on a similar thing as a pet project and still am, but it's more along the lines of "What would comprise a library that would preserve the modern world's progress and understanding if civilization had to start again from scratch?" Basically, I was looking for what books would you lock into a bunker to ensure that in the event of apocalypse the survivors could pick up the pieces (sort of a Hari Seldon's Library for Earth). I'd offer some of my suggestions, but my list is A) not as seriously researched (it's something I've farted around on in my spare time), and B) not limited in size or scope (I'd gladly include 10,000 works or more if that's what it took).
I do applaud your focus on keeping them "readable", as an Ark of Knowledge is useless if the people who find it can't make heads or tails of it (a textbook on Quantum Physics, while important, would likely be useless without enough other books to teach a lay person all the mathematic and physics principles, in plain english, to understand it in the first place). Of course, that leads us right back to the first issue again: since easier to read books are less detailed because of the assumption the reader needs to have their hand held, we lose a ton of knowledge by neglecting denser works.