If this is my first year claiming my own taxes, how do I confirm my identity to e-file? Do I put my parent's AGI or do I click on "I didn't file last year"?

From your question I make the following assumption:

Your parents claimed you as a dependant previously and you had no taxable income.

In that case you check "I didnt file last year"

I didn't file last  year if this is your first year filing.