I voted Core Books plus a couple of favorite rules or items, but the correct answer is a bit more complex.
In the campaign in which I'm a player, we have to "filter" anything we want that isn't from the core rules through our DM. It's his own world, so he of course has the final say in what fits and what doesn't. He doesn't use 3rd party stuff except for ideas. For example, my character in that game is a paladin2/cleric6 or Tyr, and I'm taking the Justicar of Tyr from Player's Guide to Faerun as a PrC, but that's pretty much the only thing my DM will allow from that book. The initiate feats are broken as all hell, and are most certainly not allowed. I like Faerun, but quite a bit of the rules isn't balanced outside of FR. (Even there, some of it is still broken!)
In the campaign that I'm running in my own home-brew world, I allow Core, Completes, stuff from Dragon, a little bit of UA, and Book of Exalted Deeds, all subject to my final approval. Stuff from the supplements sometimes requires approval/modification/shoe-horning into my world. Since it's a very heroic campaign, my usual conditions include that the feat or PrC not require you to be evil or "any non-good". Equipment and magic items outside the Core Rules are solely at my discretion, and nobody starts with magic items (that's an FR thing, IMHO). I don't allow 3.0 stuff, FR stuff, or 3rd party stuff, since it's less likely to be balanced with the 3.5 core rules. I prefer if players use materials that I own, so I can look up the item in question at my leisure (since I have a huge pile o' WOTC stuff, this isn't a problem).
-GT