I am not an expert on this; but if it's a 64-bit processor, you probably
want amd64 unless it's an Itanium, in which case you want ia64.  Look
through the literature to see if your processor has EM64T support.  If it
does, you want amd64.  See http://www.debian.org/ports/ for more information.
i386 will probably also work, but if you have more than 4G of RAM you will not
be able to exploit it to maximum effect unless you are running a 64-bit port.
I am currently running i386 with 8gb of RAM using the -bigmem kernel.
As I understand, each process becomes limited by 3GB or so of RAM. I
can't really comprehend why any *desktop* user would need/want 64bit
at this time. Although, 64bit doesn't have the java and flash issues
it had not long ago, I would not be surprised if there is still some
hassle involved.
jordan@pc-tesla ~ $ uname -r
2.6.26-2-686-bigmem
jordan@pc-tesla ~ $ free -m
             total       used       free     shared    buffers     cached
Mem:          8118       6335       1783          0        386       3534
-/+ buffers/cache:       2415       5703
Swap:         4102          0       4101