What is my occupation if I am a student with a part-time job? And which income should be listed as my primary income?

You may list your occupation as student. If you had income on a 1099-Misc in Box 7, you will need to identify the type of work you did. If you also got a W-2, it doesn't affect your return as to which would be your primary income. You can put which ever one you considered to be primary or whichever paid the most.