64-bit Windows is for processors which support 64-bit data (basically a lot bigger than 32-bit, allowing higher accuracy, faster operations with larger data and enormous address spaces). Most modern processors are 64-bit processors.
If your processor supports it, use 64-bit windows. It'll be able to run 32-bit applications, but a 32-bit windows won't run 64-bit applications.
An OEM license is for a single computer, and is not legally transferrable. Full retail you can install on any computer you like (as long as it's not on two at the same time)