If you use a CPU that supports x64, you should always install a x64 version of windows. A x64 Windows can run both 32 and 64 bit versions of software. But, a x86 can only run 32 bit software. You should download the x86 JDK.
On a side note, x64 operating system has more advantages than just addressing more RAM.
Oh ok so I should have installed the 64-bit version of 8.1 (came with both discs)? I only chose the 32-bit since I only have 2 gigs of RAM, wasn't sure if the 64-bit would be innately more taxing on it or anything.