Hi Justin,
when one talks about the bits of the CPU it refers to what type of code it can run. In your case it’s 64 bit, so the AMD64 image will be fine.
You could also check the version of Windows that your laptop came with as an indicator. If it was 64 bit you’re good to go without worry. If it was indeed Windows 32 bit you are wise to double-check, which you have done.
I think the blanket statement of “if in doubt use i386” is from the days when 64 bit was new, and many CPUs were not able to run it. In computing terms this was a long time ago and pretty much anything bought in the last five years should be able to run 64 bit code (OS, programs), but it’s always better to check.
Cheers,
Tim