hello,
I asked myself the question a few years ago. What I did is look at my statistics to see what resolution my visitors have in the majority of the case. I use fixed width towards 1024x768 resolution monitor as those are the majority of the users coming on the numerous sites I maintain.
Fluid design is interesting too and can help but you will run into some problems when it comes to websites with heavy images. Also, if you use let's say a flash gallery, you cannot use fluid as your images won't resize by themselves.
I would keep it under 1000px width and explain to your client that because they use such large monitor does not mean that the majority of Internet users do the same. In the end, they want there website to be seen correctly by the majority of users, not the 1% who can afford such sizes... (I personally work on 1600x1200
Have a good one