"Don't have an Apple ID" option will have you make one, so you can sign in.
"Forgot it" option will start you in a recovery process which at minimum takes days to verify from Apple. You need stuff to verify like the credit card on the account, and the phone number associated with your Apple ID, so they can send you a verification code. Since that number was the number I was trying to activate with my new phone, it wasn't working for whatever reason. My phone wasn't displaying any text messages from Apple while in the "forgot it" screen and I couldn't call them.
I ended up solving the problem by putting my phone into recovery mode on iTunes and reformatting. When I started setting up the phone again, I got to the Apple ID sign in screen, and the texts still were not coming through. I tried the calling option again, and then it finally worked.
Apple had me stressed this weekend, but now I am finally comfortable with my phone.