x86 = 32-bit
x64 = 64-bit

But, that's just the capability of the OS (Operating System) that's installed. Your system itself may be able to run a 64-bit OS. Find your motherboard's make and model number and see if it supports 64-bit (Google) then check to see if the CPU (Central Processing Unit) can also handle 64-bit. If so you should be good to go with a 64-bit OS. It might not be worth it if the motherboard maxes out at 4GB of RAM. Check at Crucial.com. If it will hold more, I'd consider making the jump to 64-bit. If the CPU was something less than say a 2GHz Core 2 Quad, I probably wouldn't spend the additional money on it. Just use it as is until you get bored with, or it gives up the ghost.

Note though that I personally would not use XP to access the internet. Too many holes in it that are no longer being patched to keep the bad guys out.