The next time someone asks me about books to read before residency, I will direct them here. You don't have to be a medical trainee to benefit from these, but that period of anxious anticipation between match day and orientation is perfect for buffing your attributes.
How to read a book, by Mortimer J. Adler
What better way to start learning about learning than by reading a book about reading books?
The Farnam Street blog has a nice outline of the book's main ideas. The same establishment is now hocking a $200 course on the same topic. It's probably good, but at $10 the source material is slightly more affordable.
Getting things done, by David Allen
The first few months you will be neck-deep in scut work no matter what you do. After that, though, you will have to juggle patient care, research, didactics, fellowship/career planning, and piles of administrative drek—and that's just inside the hospital. At the very least, this book will help you make time for laundry (and maybe some reading).
Thinking, fast and slow, by Daniel Kahneman
Superficially, similar knowledge to what is in these 400+ pages can be found in a few Wikipedia entries. But you would miss out on the how and why cognitive biases and heuristics are so important. Medicine and research are bias-driven endeavors, and not understanding them is not knowing real-world medicine.
Only three? Yes. If anything, the two and a half months between mid-March and July 1st won't be enough to read them all with the attention they deserve. But you should try.