Along with some informational stuff about the state of the game...
Currently, to gain legendary rank in Hearthstone, your deck has to be able to contend with some of the more powerful, yet straightforward deck-types to make it past the rank 1-25 and into the orange legend's house. Once you hit rank 5, the win-streak bonus stars go away, and you essentially need from that point on, to have ~30 more wins than losses overall.
The current powerful decks that plague the high rankings are Warlock rush, Warlock giant and Rogue miracle. Other decks are also there, but are nowhere near as prevalent as these types.
If your deck can consistently pull out a >50% win-rate against these types of decks, then you'll eventually make Legendary if you keep at it, the experience gained from a loss against one of these decks will help you the next time, and eventually you're able to perfect your game to the extent where you either know you're going to lose, and need to adjust/change your deck, or know how to win, and can chalk losses up to things like "bad starts" or "crazy RNG" that evens out over time.
It's a fairly cheap deck, only one legendary and three epic cards - so most people should be able to afford it, or at least something similar. Though, if you're really short on card options, a warlock rush deck might be a lot cheaper and off the top of my head doesn't require any legendary/epic cards - Leeroy is optional there.
If you're playing Hearthstone excessively, you'll probably be able to plow through the daily quests without any problems at all - either by doing arena or simply playing one of your constructed decks. However, for the slightly more casual players, this isn't always as easy to come by - and it's quite "important" for your gold balance in Hearthstone to make sure you clear out the daily quests, at least by the time there's 3 of them, or there'll be "missed gold".
Now, I've decided to share my "mindless dailyquesting" strategy here, which usually gets the dailies sorted in a matter of minutes while I'm primarily focusing on ... well ... anything else to be honest! I've made mindless agrodecks, and switch the play to "casual" to avoid messing up my played rank, and just have fun seeing how disgusting I can be with primarily only spamming damage to my opponent's face.
Here's a sample of the basic decks I use, I've edited them slightly to attempt to only include basic cards, with a few rares sprinkled in here and there, and the odd epic. But, to be honest, you can replace them with basics and still do relatively well. You should note that this won't make friends, and (apart from the hunter deck) they probably won't do well trying to get high on the ladder, but they'll get the daily quests done usually quicker than "serious" decks would.
Now, the basic principle is really just to try to hit the hero for face damage as much as you can and don't trade minions unless your opponent has a huge damage potential with one of them. Everything should really be straightforward here, one note with the mage deck is to always save your frostbolts for when you have 1 or 2 ice lances for the bonus damage.