If you been playing hundreds of arena games, you'll end up with huge profit. Good examples are Kripp or even Ek0p. Since they're popular streamers. They've gathered over 50k gold and every legendary card from doing arena runs for many months. 12 wins can give you 400 gold+2x packs+dust+legendary golden card. Not very likely. But the rewards can be insane.
If you really wanne be a free-to-play player. Researching arena guides is a must. Its really the best and fastest way to get all the cards for free. And people have already done it before. So its not impossible. But it does take time and dedication. I've done 5x arena runs on 1 day because of profits. And im not the best arena player. The alternative is to pay, give or take 300$-500$ to get everything. Depending on how lucky you are with opening packs. But you really dont need every card to be succesful in this game. Just buying 40 packs will get you quick started. And who knows you might open up multiple legendaries. I've seen single packs with triple legendaries.....
Right now Naxx is out. And you need 700 gold to unlock the wings with the new cards. And you really want the new cards, since some of them are very very strong. Not to mention they include legendary cards.
If people want more advice or play against me:
BattleTag EU: PaiMei#2114