Is this game a moneypit where you want to keep buying more and more? If you buy some sets do you have enough to introduce a new player to the game?
How much money do you need to spend for this to be playable with two players
big money pit? not really, especially once you catch up.
to answer the question posed in the title.....as much or as little as you want to spend. If you just buy the core set (like $30-$40 depending on where you get it) you can play the game with 2-4 people forever. if you want to add houses or add cards for those houses then it obviously adds a little more money to the game. the good thing is that between the product info page, the community card databases, and these forums you can fairly specifically target what and when you want to add cards.
once you do get to a place you are comfortable with and decide you just want to maintain with new product its only $15.00 a month (roughly) to buy the new chapter pack.
I'll echo what Lars said. My friends and I played for a couple months using just the just the core set and the greyjoy box. We had a great time and alot of fun (3 and 4 player). However once we started buying packs to customize our decks more we have all spent a couple hundred since. Of the 4 others 2 of us just bought everything, 2 others have spent around 150 and one guy is just buying the box sets and the new packs. This has added alot of fun to the game if only by giving us more toys to play with. I'd say you should be fine if you only want to play with the core set but if you are looking to spend alittle more but not alot I'd get the current cycle packs ( Brotherhood Without Banners ) and perhaps the Lords of Winter (Stark) and Kings of the Storm (Baratheon) boxes. That would run you about $110 more if you buy from the various online discounters. These packs/boxes give you alot of great cards and have easy ways to customize the starting core decks to help them play better. If you want to browse spoilers for the packs I've got a spoiler with images , a searchable spoiler , and a deckbuilder at my site. It might help you narrow down some purchases to save money.
Some options for you:
1. One Copy of the Core Set ($40 MSRP)
This will give you four 45-card house decks (with 4 7-card plot decks). This will give you six possible match-ups right out of the box. You might want to shuffle around some of the plot cards, as some of them are best in multiplayer. You could also build two full sized 60-card decks out of a single core set, but deckbuilding options will be limited.
2. Two Copies of the Core Set ($80 MSRP)
This will give you a greater degree of deckbuilding possibilities in each house, and two copies of every plot will give both players freedom of choice in plot decks. For variety, this is probably the best deal: this will give you the potential for a couple of different builds in each of four houses.
3. 1 Copy of Lords of Winter ($30) OR Kings of the Storm ($30) OR Princes of the Sun ($20) + 1 Copy of Lords of the Winter ($30) OR Kings of the Storm ($30) OR Princes of the Sun ($20) ($50-$60 total)
This will give you a greater depth in particular houses while sacrificing the variety of multiple houses. For example, if you were to buy Lords of Winter and Kings of the Storm, you'd be able to try a few different Stark builds and a few different Baratheon builds, and swapping a few cards between the sets would increase your options. NOTE: If you elect this option, you won't have a) rulebook, b) power and gold tokens, or c) multiplayer titles. You can download a copy of the rulebook from FFG, and you can use some substitute (pennies or peanuts) for tokens. You can make proxies of the multiplayer cards.
4. 1-2 Copies of the Core Set, plus Lords of the Winter/Kings of the Storm/Princes of the Sun ($90-$140 total)
This would give you a broad collection, with strong deckbuilding possibilities for every house (except greyjoy and possibly martell), and very specialized build possibilities for Stark and Baratheon (assuming you got Kings of the Storm and Lords of Winter).
Personally, if you're just starting out, I'd just recommend getting a single core set. The 45-card decks aren't optimized, but they are full of very strong, foundational cards, and allow for some create play experiences. From there, you can either expand generally (through an additional Core Set or Chapter Packs) or specifically (through the deluxe expansions for Greyjoy, Martell, Stark, or Baratheon).
Just a core set is good starting point and then I would recommend Kings of Winter and Kings of the Storm. I own every card at least one copy for the game and it only took me a year to do that. But you don't need that many to play or have tons and tons of fun. One core set is plenty to play with for two players and then go from there.