How important is the choice of dissertation committee? I am currently a PhD student and I need to choose a dissertation committee as I will be graduating soon. (I already have a postdoc lined up.) It seems the only function of this committee is to read my thesis, attend my defense, and decide whether to grant me a PhD. 

Assuming my dissertation committee serves its purpose and grants me a PhD, what further relevance do they have? How should I choose my committee? In particular, is my committee still important after I graduate?

The reason I'm asking is because I don't really know who to choose. It seems like I should just ask whoever in my department is available. Should I be considering other factors? For example, it is good to have "famous" researchers on my committee?

I asked my advisor and she didn't voice an opinion and said it was essentially up to me who to choose.
I can share my perspective as person who recently completely a PhD thesis (May 2015). I think that choice of members is something which should not be taken lightly. I would think about a couple of key components. Which members of the faculty have interests/experiences in areas which are potentially interested in pursuing the future? They could be useful in terms of networking in the future.  Are their members of the faculty who you have spoken to about your project in the past who might be able to bring a bit of familiarity to defense, this is potentially important in terms of them being able to write a stronger recommendation letter. I think the last thing to think about are the different components of your thesis and selecting members who can best ask you about the individual sections in your thesis. 

Best!