I've been reading the forums trying to get a feel of what my initial purchase is going to be for two people that will always play together. 3 cores total (and one of each chapter pack or deluxe box) is enough to cover two people. That is, as long as you both don't want to play the same faction at the same time. There are a few neutral cards you might have to share occasionally, but that should rarely come up and is very manageable.
We also love to play Androud Netrunner and enjoy building decks. In fact, when a new data pack released, we would each buy one so the card pool was always the same for each player. This kept the choices and building options fair.
With AGoT, I see people saying to start off with 2 or 3 cores (as opposed to starter decks if your intentions are to deckbuild down the road).
Is that 2 or 3 cores per person or for two player?
But ultimately it's similar to Netrunner. If you want full access to all the same cards, you will need 3 core sets and 1 of each chapter pack/deluxe box per person.