Disclaimer: I am not a lawyer. The following is based on seminars I’ve taken on copyright law and discussions with colleagues who have studied and/or practiced copyright law. The information may be out of date or based on a misunderstanding. It is always advisable to speak to a practicing lawyer.
This is an excellent question, but also one that’s rather difficult to answer. The reason is because there haven’t been enough test cases to set the boundaries. Strictly speaking, all the quotes you are planning to use are probably subject to copyright unless they are old enough to have passed into the public domain. If you were just planning on using a few quotes as epigraphs for longer essays, you wouldn’t have a problem so long as you cited them properly. But you want to publish and sell an actual book of quotes. This makes the fair use rationale much more difficult to maintain. I know lawyers who insist that you are technically free to use the quotes and others who assert with absolute certainty that you would lose in court. And frustratingly enough, those positions aren’t mutually exclusive. You can lose in court even when you technically should not.
Because of this lack of clarity, a convention has long been established regarding what to do in cases like this. Rather than risk an infringement suit, write to the copyright holders asking for permission to use the quotes in which you are interested. In many cases, the copyright holders will not be the authors of the work you are quoting. Be clear on exactly what you want to use, how it will be presented, and how the copyright holder will be acknowledged. Regarding the last of these, one standard thing to do is have a list at the end of the book completely citing the sources of the quotes. Some books are explicit that all quotes were used by permission, others are not. Odds are, however, that they all got permission. It’s just easier that way. But like @ETpro said, look at some other books of quotations to get an idea of what to do.
As I understand it, though, most copyright holders are fairly willing to go along with things like this. The purpose of copyright, after all, is to encourage distribution. Plus, they generally have nothing to lose so long as you have asked for permission (thereby reaffirming their copyright). Good luck!
P.S. Here is an eHow article on obtaining permission from publishers.