Hunter is one of the easiest ones to start with. The Adventure Packs are the best use of gold early on, if you don't want to just shovel real money at Blizzard. A number of cards from them are staples in a lot of decks for one class or other (or for all classes, like the Sludge Belcher). It will seem slow, and it is, but it's worth it if you think you're going to stick with the game. 13-15 of the 30 cards from Naxx are used in decks constantly. Blackrock cards aren't as ubiquitous, I think there are only six or seven that get used constantly but it'll allow you to do a themed deck which will still work reasonably well in low-ranked play.
Whether you spend gold on arena or on packs kinda depends on what you end up liking from the game. You won't do WELL in arena if you're not familiar with the game, but you'll do better than you're likely to in ranked play (and there's basically no reason not to do ranked play rather than unladdered, since ranked can give you rewards now). You won't get as many cards as quickly, and the fact that you don't know which set you'll even get a pack for now is a PITA, but it was my preferred way to spend gold before. But it really depends on your tastes.