Buy the adventures with cash. $50 should get you BRM and LoE. You can't buy packs for these cards, the only way to get them is by buying the adventures, and the gold cost is prohibitively high. If there's any money left, buy a few classic packs. Then just spend your gold on packs. For a good long while, classic packs are best for you. There are so many important cards here and you'll basically need to have the classic set if you want to be a long-term player. These never rotate out, it's a solid investment. Spend dust crafting cards you need from TGT and WotOG, but buy classic packs for at least your first 100 packs, probably even 200. Then once you have most of the important classic cards, start buying WotOG packs instead. Never buy TGT packs, too few cards from that expansion are playable.
If you end up liking the game enough that you think you'll play it seriously, do yourself a favor and spend $100 on packs. This will vastly improve your collection and allow you to make a number of top tier decks. It's worth the investment if Hearthstone will be your main game for a long while, and that amount of packs will pretty much set you up to play for legend rank. When you have the means to make a few of your favourite decks, you don't really have to spend any more money as you can slowly build your collection through quest rewards and stuff.
