The easiest way to check if you have a 64 bit processor is to download CPU-Z from http://www.cpuid.com.
CPU-Z is made available as a zip file, unzip it and then run the exe it contains. The program will collect information about your processor and then under the CPU tab, in the instructions column, see if you have any of these AMD64, x86-x64 or EM64T. if you have any of these then your processor is 64 bit.
If your PC has a 64 bit processor then you will be able to run the 32 or 64 bit version of the operating system of your choice. Currently there aren't a huge number of free 64 bit applications for Windows. Details of those that are available can be found here.