From what it seems like you want to do, the most important thing is that when you get to the screen in the attached image below, select "Set up as new iPhone". Otherwise, just follow the prompts, including logging in with your Apple ID. Once your phone is up and running, go to Settings>iCloud and if you're not already signed in, sign in and enable Contacts and Notes (and everything else, if you want to) and that should do it.