I am trying to install windows server operating system on a DELL optiplex desktop GX600 series, During the installation, In the first step I was asked to choose between: 1)Windows 2008 X86 Architecture OR 2)Windows 2008 X64 Architecture
Now, how do I determine what architecture my Dell desktop is built on and which OS installation option should I choose?
This entirely depends on the applications you'll be using on your desktop and whether they support x64 or not.
Make a list, and do some research, but if you're unsure, and don't have a good reason to go x64, I would go x86.
As epophwolf mentioned you need x64 if you want to fully utilize more than 3GB of RAM. However, there are other considerations as well. Firstly, does your machine have a x64 processor? If the machine fully supports x64, that in my humble opinion is the best way to go. Most software is now compatible with x64 OSes, and from an x64 development environment, you can develop for both. Also x64 Windows OSes are capable of better utilizing the functionality of the processor, and I've found it to be faster than x86 on my machines.
I've just checked on the Dell site, couldn't find any references to the GX600 but there weren't any Vista/W2K8 drivers available for the GX620/630 in 32-bit, let alone 64-bit, flavours.
Download CPU-Z and run it on the current system. If your processor supports EM64T instruction set (assuming it's an Intel, dunno about AMD), then you would be able to run x64.
I have been running x64 on two machines, one Server 2008 and the other Vista Ultimate, and I have had no problems, or at least none that come immediately to mind. I recommend 64-bit if you want to use more than 3.25-3.5 GB of RAM.