The Player’s Handbook
Although this question is too subjective for SE, there are some arguments to why the PHB is the best option of the three core rulebooks. The overriding reason is that it is all you need to play.
The adventuring, combat, and spellcasting chapters cover the core rules of the game in roughly 30 pages (spell descriptions excluded). These are the most important chapters of the game, because they are the general rules governing all things.
The PHB supplies player options, which are required to play the game, and a few monsters – mostly animals – are available in the back of the book as a mini-Monster Manual.
In contrast to the PHB, the DMG provides optional rules and guidelines for DMs to craft intricate and interesting worlds, but none of the base rules and the MM provides more monsters (and nothing but). Clearly, the PHB is the only one of the three core rulebooks that stands on its own.