"Display PDF in browser using…" is grayed out, so I can't uncheck it.
Is it grayed out AND checked? I think it can only be grayed out when unchecked.
Concerning the opening of PDF, I always first see it in the browser then save to desktop. There you can click on any file, then hit command-I (get info) or go there with a right click or control-click and change open with to Preview and then apply to all. This way all pdf files on the hard drive will be openable with Preview. I personally recommend Adobe Reader though for better functionality. Safari has an option of opening downloaded safe files like pdfs. Most people recommend to uncheck it but you might like to check it and see how it goes. Also try Roger's advice - it looks like a pretty sound one to me.
P.S. I have a sneaking suspicion that Joe is right too.