Doctoral committee members consider it a part of their responsibilities to suggest research leads and specifics bodies of research. Most established researchers are very knowledgeable about their fields (do not get intimidated; it comes from years and years of reading and conference-going). They may recommend many different resources, names, and specific books and papers. Such recommendations can be anywhere on a continuum from "I vaguely remember something that might be related to your topic" to "This is the essential research you cannot afford to ignore in your dissertation." Much of doctoral students' confusion comes from their inability to correctly place recommendation on a scale between these two extreme points. When in doubt - ask for clarifications!
It is rude to ignore or forget your adviser's or committee member's suggestions; it is also counter-productive, because they wish you to succeed. However, if you have good reasons not to follow the advice, state these reasons as clearly as you can, and discuss them with the advisor.
Some committee members will disagree with each other about the direction and theoretical foundations of your research project. This is very normal; scholarship community thrives on disagreements and discussion. The best strategy for you is to engage the disagreements on the pages of your dissertation. However, if you fell a dispute becomes less professional, and more personal, talk to your main adviser. It is the advisor's responsibility to negotiate any conflicts within the committee in such a way that it does not harm your progress. To avoid finding yourself in a difficult situation, be deliberate and careful about forming your committee in the first place; make sure your main advisor has good working relationship with the rest of the committee.