|Zach Klopfleisch Venture-Lieutenant, North Dakota—Fargo|
Core Rulebook and Advanced Players Guide will give you the vast majority of the rules you'll ever really need. Other books will allow you to tweak characters here and there, but those two will give you enough to do just about any concept. The other hardbacks (Ultimate Equipment, Ultimate Magic, Ultimate Combat, Advanced Class Guide, Advanced Race Guide) are all great books, but are more niche. Every character you make will have the majority of his features in the CRB, a significant plurality of your characters will have stuff from the APG. The rest aren't nearly as universally useful.
Inner Sea World Guide will give you all you need to really understand and get the most out of the setting. What's the deal with the Andorans and Chelaxians? Who are these "Varisians" in Magnimar? You get so much more out of the scenarios, and things are much more easy to understand, when you know what's going on in the world, and the ISWG gives you that. Inner Sea Gods is great for understanding religions and divine casters, with plenty of great rules, but it's not nearly as universally useful as the ISWG.