If you're worried about memory usage, go with 32-bit (32-bit applications tend to use less memory than 64-bit applications). If you want to take advantage of the various extra features of the CPU (extended/extra registers, instruction set extensions, etc.), and you don't care so much about memory usage, I would go 64-bit.
EDIT: 6 GiB is more than enough for a typical desktop user. As TobiSGD said above, it's easier to go 64-bit if you want to be able to address the full 6 GiB, but you can use it with a 32-bit kernel, as long as it's PAE-enabled.
As previously stated, it really depends on what you want to do with your machine. :-\
Last edited by MrCode; 05-04-2011 at 12:15 PM.