If it's only 2GB RAM then go 32-bit. 4GB and higher go 64-bit.
To be honest though RAM is pretty cheap again so I'd strongly recommend grabbing 4GB anyway to give your system plenty of breathing space.
BUT what are your exact specs? What dual core is it? What RAM do you already have?
And what do you mean by Windows HP? Do you mean Windows XP (Windows XP 64-bit isn't very good - poor driver support and now very old), or is your computer from HP?