So I had completely forgotten you could play this game for free because everytime I see a stream or read about it, money is involved somewhere. Anyway, I'm just wondering how far can I realistically play this until/if I get to a point where I'm seriously underfucked for not spending money?
Depends if you're talking arena or constructed. Arena you can technically play forever for free, although it's generally unlikely that a new player has the skill and experience to do 'infinite arena,' i.e. win enough games in each arena run to make back the money it costs to enter. You need to average seven wins per run. Until you can do that, expect maybe one arena run per day and sometimes days where you simply can't play arena because there's essentially no way to earn gold besides your daily quest and then arena itself. This is why telling new players to 'just play arena' is really pointless; new players can't actually access arena regularly, there's simply a limit to how often they're allowed in due to the 150 gold cost and the fact that you typically get 40-60g per day from the quest (and often have to spend an hour or two in casual mode just completing that with a shitty basic constructed deck).
In constructed, unless you're content playing just the one cheapest deck from the dozen or so top tier decks, the game is not free to play. You
canmake face hunter with very little dust, but it's the absolute noskill bottom-feeder deck and you'll be regarded as the most spineless scrub in the world if all you play is face hunter. It's the easymode newbie deck of Hearthstone and also incredibly irritating to play against, as well as really boring to play as there's virtually no strategy or decisionmaking involved. But it's a good enough deck to take you to the top, so that's essentially the option for F2P players. If you want to play real decks, you simply have to invest money or play arena for a few months first.
I'd say the minimum amount of money to get a few proper decks (without first playing arena for a few months) is a hundred bucks. Any less and you'd have to be lucky to open some necessary legendaries from packs. You need to invest $50 just for the two adventures as those cards can't be obtained any other way (you could probably get away with just the first wing of BRM as few decks use the cards from the other four wings, but I'd recommend getting the whole thing anyway).
To actually get, say, five or six of the best decks around, you're looking at something closer to $200, with all of it spent on packs and disenchanting every card that isn't used in one of the top tier decks. And you'll still have only maybe half of the decks dominating the meta, if even that, which means many of the decks will be difficult to play against as you've never tried them yourself. The difference between knowing a deck from playing against it and being familiar with it from owning and playing it is huge, and you're probably never seriously on equal footing with the top players until you have all cards yourself, which takes either hundreds of dollars or many months of regular play.
Hearthstone is only F2P in the technical sense of not requiring you to buy it or pay a subscription fee. It's pay-to-compete, and the barrier of entry is such that getting anywhere without spending money is almost completely unrealistic. At this point in time, with two adventures each costing 3500 gold to unlock, doing this with gold earned from playing the game is basically not possible. You could potentially get all the important classic and GvG cards playing arena very heavily for maybe two months and spending all excess gold on classic packs, but earning 7000g through play is something that would take even highly skilled veteran players something like four months to do. I have never heard of a new player obtaining all cards by playing the game, not counting people who started back when there was just the classic cardpool.