As the GM you have more control, and I'd simply suggest that you disallow everything but the core rules, requiring everything else be okayed by you before coming in.
There's a lot of good advice in this thread, but the piece that has been echoed by many to place limits on character options is one I can't agree with. I DM'd 3rd Edition for almost the entire length of the game's published history, and only let D&D slide onto the back burner for non-gaming reasons (RL got too busy) just before the transition to 4E. During the entire time, I let players choose any options present in any WotC book or magazine, and probably would have been cool with any d20 3rd-party material too, but my player's never asked. I firmly believe in saying "yes" almost 100% of the time. I very rarely say "no".
This never caused more than minor problems that only briefly interrupted action time, if even then. This worked for me because I am a very laid-back DM who can't (or, well, won't) memorize rules and dislikes looking up rules mid-game. Like others have suggested above, whenever a rules question came up in game, I made an on-the-spot call, and if anyone was bothered by it, we could research/discuss it between sessions and I might make a new call. My player's learned that trying to meta-game didn't work with me all that well, because I would simply adapt my story to whatever they did with their characters.
I only had two problems, one that bothered me and one that didn't. The easy problem that wasn't really much of a problem was the one player in my group who we all suspected of both cheesy powergaming and fudging rolls. He played a suspiciously successful wizard who rolled lots of high numbers. I simply decided that his character had become an infamous wizard, and like famous Wild West gunslingers, other powerful wizards and creatures came out for him so they could become famous for taking him down. I never killed his character, but threw big stuff at him while other baddies occupied the rest of the party. He had a great time battling these powerful foes, and he didn't outshine the rest of the party (by making them feel unnecessary) while they fought other foes. My players, except for the power-gaming cheater, caught on to what I was doing, and it became fun for them to see what I would throw at him next to "distract" him. More than a few times the party had to save his bacon after they dealt with the other foes. But it was all in story and we all had fun, even if I felt slightly guilty for targeting him separately.
The other problem that did bother me was a player who joined my group only briefly, and asked if he could use a character class he created himself, a "candle mage". I was leery, but didn't want to say "no", so I let him, and it was (as you might expect) ridiculously over-powered and weak of concept . . . . to an embarrassingly obvious degree that angered all the other players and did disrupt the game. And to this day (not that I DM much anymore) it is the only limit I place on my players, is that I don't allow homebrew character options (unless *I* create them).
While I am generally opposed to placing limits on character options, if you are doing so for story reasons, such as creating your own campaign setting with a different feel and tone than standard D&D (like, say, Dark Sun), then I say go for it!