iPhone migration

So I'm trying to understand iPhone migration. Now, I understand Quick Start, but it's not completely clear when to use it.

If I buy a phone from Apple, they send you the phone already set up with your carrier and your phone numner. I understand that when you turn it on and set it up, boom, it replaces your old phone. BUT, when do I do Quick Start? Do I do it before I change carriers, or after I do so, or does it matter? I mean, if my old phone is disabled after I switch carriers, is it even going to communicate with my new phone?