Don't get any sort of student visa in advance for your trip. You want the regular short term visitor visa, good for up to 90 days, assuming you will have a US passport. That way you will be eligible for any of the assorted types of JR passes, with a student visa, you won't be.

Note that if you want the whole country JR pass, you have to buy it in advance before entering in Japan.

Maybe this thread will get better responses in the Japan forum, I'll alert the mods.