Hello, I think 960px is your best choice for your template width. However, there are designs that exceed 960px into the 1000's, no greater then 1024, to support spacing/padding on the left & right sides of their template. For your .psd I'd say set it's width to about 1200 to give you some working space then lay down guides in your .psd to design your theme keeping it's width within 960px. After a .psd has been converted to html a coder should be able to define a new width or make it responsive for larger/smaller resolutions as he needs.
It's not mandatory to do it like this but it's the general idea I think.
Thank you both for the fast replies!
So I start by putting the width to 1200px. So far, everything is clear. But then, what do you mean by "lay down guides"? Should the template not exceed 960px?
It's the first time I make a real PSD template so I don't know so much about that.