Efficient Free-to-play Guide to Hearthstone by takeeacy from Hearthstone Players site.
A nice guide for new players starting now after the release of Naxxramas and I will say also a good read for people still building up their card collection.
Personally, I find the daily class specific quests to be tougher now as more and more players have better card collections so I recommend to build/craft a competitive deck like Zoo Warlock or Midrange Hunter first and foremost. Those are easier to build/craft with 0 legendaries and epics. With Zoo, you can win very fast but I find more opponents playing taunt minions which can stop Zoo in its track easily. Hunter seems more versatile and was the first deck I went for. Check out what cards are not used in all competitive decks or MaSsan's disenchant guide and disenchant those. For the best value, crafts 1 of each required rare first. (Edit#1: After which, it is up to you if you want to complete the deck with all required rare-s and missing commons. I personally will not craft commons and wait for them to come from packs instead. For rare-s, I only craft 1 of the required rare and if the deck uses a single rare, I will leave out crafting it too.)
With that 1 competitive deck, you can earn gold faster and more efficiently through matching daily quests as well as 10 gold from 3 wins. You will even be able to climb the rank ladder. Keep all your gold (from initial quests and achievements) and only use it for Arena specifically to complete daily quests that involves other classes. As you win more games in arena, the entrance fee of 150 gold decreases and on top of that, the daily quest helps to pay for it too. You theoretically get to use all the cards in Arena, provided you draft them, so it reduces the disadvantage of your otherwise small card pool and lack of Naxxramas card.
I keep doing the above and slowly build a competitive deck for each other class one by one, starting from the next cheapest deck, with the goal of being able to do the class specific daily quests without arena. (Edit#2: Again take note of your crafting strategy like in Edit#1) It takes around 5-6 classes to be able to cover them. (Edit#3: Based on the class combination and assuming you go for the 2 easiest competitive class, Hunter and Warlock, I will go for Rogue + Shaman/Mage + Paladin combination which should be the least amount of classes required. Druid decks generally uses a lot of Epic cards so it's great to avoid it first IMO. Edit#4: I went with Mage instead of Shaman because you can build the Aggro Mage which shares most of the cards with Aggro Rogue. ) At this point, if you have gotten good enough at Arena with consistent 7+ wins, then by all means, stick to Arena. I average 4 wins so far, thus I think it is more time efficient to go for packs instead. 3-4 wins is worth a pack plus maybe some extra gold, dust or card and with that, I will rather spend 300 gold on 3 packs then 2 arena runs.
With the daily class quests settled, it should be easy to earn gold now. I will then go for unlocking the Naxxramas wings. If you ever want to spend money on Hearthstone, I recommend buying the bundle right at the beginning as it is just more efficient and saves you a lot of gold unless you have already amass a lot from tons of good arena runs. The cards are easy to unlock without the need to use a competitive deck and a lot of the cards go straight to most of your decks. The cards are nice but I don't think it is a good idea to drop 700 gold on each wing as it takes a lot of time for players starting out. I rather keep the gold for Arena runs to help complete daily class quests in the beginning.
The above is my guide to players starting out in Hearthstone now. I kind of begin playing more when Naxxramas arrive so I was also starting out late. The guide highlights some of the difficulty I faced so if I were to start over, I will probably do it as stated in the guide.