Tally another vote for Core, APG, and Bestiary 1- though it's worth noting that Bestiary 2 contains updated rules which supersede Bestiary 1's. Which is why I'll put in a second tier of "should-haves," especially if you're the GM: Bestiary 2, GMG, UM, and UC. UM and UC are full of rules variants, yes, but each one has many new class options that one should know about even if one doesn't use the variants. Magus is a prime example of that, but also on the list would be the Cavalier Archetypes (APG doesn't have any, and UM didn't have any since it was magic-focused) and some of the other Archetypes in UC (the Tactician Fighter comes to my mind- think Fighter using the Cavalier's Teamwork tactics and feats, which IMO is one of the best features of the Cavalier class).
On a side note, I've seen several people complain about UM and UC being "broken," but I just don't see it. I can only assume these people play the game very differently from me, because I haven't had a problem with anything from those books so far. Admittedly, I only play once/week and ran a high-power, high-magic game (which is why I suggest the people considering those books "broken" must be used to very different game styles from myself).
On a side note, I've seen several people complain about UM and UC being "broken," but I just don't see it. I can only assume these people play the game very differently from me, because I haven't had a problem with anything from those books so far. Admittedly, I only play once/week and ran a high-power, high-magic game (which is why I suggest the people considering those books "broken" must be used to very different game styles from myself).