Yes, you apply for the individual NPI number. And while you're a student, you can't list a license (because you don't have one yet), so make sure your taxonomy code is something like 'student in accredited program' or something. And then once you get your license, you can update it to indicate that you're in whatever field you're doing.
And be sure to put your program's address, not your personal one. This is publicly available information on the internet, and you don't want random people to know that information. You can put your own phone number--this will make it easier for pharmacies to get in contact with you--but, again, it's probably better to put a quick contact number with your program.