x64 and x86 are identifiers for different types of processors.
x86 is for 32 bit, and x64 is for 64 bit processors.
It is important to get the right one, because the software contained in each build (64/32 bit) is made for the kind of computer you have. Not knowing what kind of software you are running right now, I don’t think I could tell you how to find out. Look for a detailed hardware overview. The device manager in Windows is a great place to start. The BIOS might be able to tell you something as well.
I don’t know about all of the issues with the server OSs, but I do know that Windows has been stuck in an awful 64 bit catch-22 for the longest time: there are no drivers for 64 bit because no one uses it because there are no drivers… Buyer beware.
If I had to guess, I would have to say that a general purpose tower that you are trying to put Windows server on is of x86 architecture.