I am a student. I just want to have it useful for school for necessary reasons. I have known of WolframAlpha for it's great computing engine. I guess I will look into the additional services it provides. Also, I need apps that don't require internet to be used. This is so I can use them at school since the school's WIFI is locked. D=
As a student, the apps you have listed should all be very useful. As the year goes on it could be a good idea to search the app store from time to time to see if there are any apps directly related to the topics you are studying.
Do other students use iPods? And what about your teachers?
Well, I learned that my school is very strict on electronics and won't even allow them for education. Only one teacher in the whole school will allow me to use it and that is for Photography. So, what would you recommend for that? They can be free or paid.
You're pretty limited if your school won't allow you to use it. That being the case, you might get by with an ipad or mini. Schools can be pretty funny in how they see devices and their worth. Apple didn't help any by naming it an ipod touch.