When I first looked at running pathfinder I thought I should only allow core books because that is what paizo has to draw from then add class as they come out in the pathfinder books, but my players seem to want more options, Will allowing splat books make it so that the players can just walk though the game, I mean I know I can always add stuff to make it hard if need be but just curios about as written
It will apparently be necessary to have at least something more than the core books, as the AP uses the full SRD, which actually contains more than is in the core books. For example, a few gods discussed in the player's guide list domains which are listed in the SRD, but not given in the PH (i.e., Community, Glory, Charm, Liberation, etc.). So my first instinct would be to have them all grab copies of the SRD, at least.
My preference has always been to stick to the core elements and, if one of my players desperately needs to be a Reborn Sould of the Doomed Deity, then he can freakin' roleplay it.
At the base level, though, it's going to be easier to add stuff than take it away, so I recommend starting out with the core and adding in things as you go along.