Assuming you are using standard X86/AMD64 hardware, you have the following options:
1) Windows XP/Vista/7
2) Mac OSX
3) Security Enhanced Gnu/Linux (Many versions are available)
4) Open Solaris
5) Open BSD/Free BSD/Net BSD
There are other options of course, but these are the best choices in my opinion, due to having the best hardware support (note that OSX runs well only on hardware manufactured by Apple). In detail my comments are:
1) Windows XP/Vista/7 - probably the worst choice. Microsoft has shown an inability to issue timely security patchs. I cannot recommend this product to anyone.
2) Mac OSX - with minor modifications it is fairly secure (but the Safari web browser should be replaced with Firefox, Opera, or some other browser). Apple has shown some problems with patching, so it may not be safe enough.
3) SE Linux - many versions are available. Linux has the best hardware support of the available operating systems. It is completely customizable as source code is is freely available. Good solid choice. Patches are available quickly, and if you have the in house programming talent you can patch it yourself.
4) Open Solaris - several versions available. Good, solid OS. It is completely customizable as source code is is freely available. Good solid choice. Patches are available quickly, and if you have the in house programming talent you can patch it yourself.
5) Open BSD/Free BSD/Net BSD - the Open BSD version was written specifically as a secure OS, and this is probably your best choice. It is completely customizable as source code is is freely available. Patches available quickly, and if you have the in house programming talent you can patch it yourself.
I would strongly recommend OPEN BSD. If you contact the Open BSD community, I suspect that they would be more than happy to assist you.
On a personal note, I run Linux and OSX myself, but I don't have your security requirements!