If you are a player, the Pathfinder Core Rulebook and the Advanced Player's Guide are must haves.
If you plan to GM, the Core Rulebook, APG and Bestiary 1 is the required core, but of course I would add Bestiary 2 and the Gamemastery Guide to those, sooner rather than later.
In the nearly one year since its release, the APG has become a default book at the overwhelmingly vast majority of Pathfinder tables. I think you should pick it up either way. The Adventure Paths and modules, furthermore, assume it is in use at the table.
While Ultimate Magic and the soon-to-be-release Ultimate Combat may someday become a default assumption, right now, Ultimate Magic has not yet taken on the ubiquitous nature that the APG has earned in terms of popularity.
The last thing to get? Why, Episodes 1-14 of Chronicles: PFPC of course! We don't attempt to cover the whole wide world of gaming. We cover Pathfinder and that's it. And we do it in-depth. If you are a Pathfinder GM, especially, you will find the podcast highly informative.