With the release of the Wrath of the Old Gods expansion set and a brand new play mode it's a confusing time for everyone, but none more so than returning players who may suddenly find their old decks are no longer playable or new players who will be playing Hearthstone for the first time trying to work it all out alongside playing catch up against what can seem like insurmountable odds. It is for you that this guide is intended so take heart and listen well. This is also a first draft, if any other posters have anything constructive to add then don't be shy with it and if it's sound advice then I'll happily add it to the guide.
Our aim here is to give you relatively powerful playable decks that will allow you to play with whichever class you have quests for or favour without you having to craft a single Epic or Legendary, not only that but as you acquire more dust and cards these decks can be matured into their final refined versions. However even as they are these decks should allow you to play competitively, you will just be punished much harder for misplays than someone playing a more expensive version.
For the new players
My first piece of advice to anyone new would be to buy the Adventure's rather than packs of cards. They contain powerful cards some of which create new deck archetypes for you to build or give you a solid win condition. Unlocking them with gold will take you a significant amount of time however at 700g a wing so if your both new and intend to be entirely F2P this may not be viable if you intend to actually enjoy yourself.
If you intend to play entirely F2P then the play mode for you is the Arena, it's daunting but there are websites which can help you construct your decks and once you "git gud" then the gold you spend here offers returns that may even let you play the Arena infinitely for free, thus giving you something to do whilst you build your collection.
The decks!
If your brand new to Hearthstone this is the best deck I can come up with from the Basic cards.
http://imgur.com/jynv437
It's a Mage deck which plays what are considered the most powerful Basic cards. If you can keep control of the board then Stormwind Champion and Frostwolf Warlord should win the game for you.
You can also try this Warlock deck which was designed by Mormolyce.
http://www.hearthpwn.com/decks/123222-basic-zoolock
Whereas the Mage is more of a Midrange deck, this list is an Aggressive one. Flood the board with your cheap minions and replenish your hand with your Hero power. Only make minion trades when they represent value (as in you get to keep your minion on board or let you keep control of the board) and deal damage directly to the opposing Hero whenever you can.
The rest.
http://imgur.com/PsXuRq5
http://imgur.com/RAMN1xP
Classic Zoo by Mormolyce http://www.hearthpwn.com/decks/70591-basic-zoo-lock
These are shells for the cheap but powerful decks that are just off by a few cards, if you particularly enjoy a certain deck then spend your dust fleshing it out with the Epics and Legendaries it needs and you will have a deck that can hit Legend.
What am I missing?
Earlier I mentioned that these decks were off by a few cards, well here's what they are missing if you want to complete them.
Druid - Twin Emperor Vek'lor and Brann Bronzebeard.
Hunter - Quick Shot, Snake Trap and maybe Call of the Wild.
Mage - Flamewaker, Antonidas and Arcane Blast.
Paladin - Tirion Fordring, Keeper of Uldaman, Leeroy Jenkins and potentially a Blood Knight.
Priest - Twin Emperor Vek'lor, Crazed Worshipper and Entomb.
Shaman - Doomhammer and Elemental Destruction if you want to play a slower list.
Warrior - For C'thun you want Twin Emperor Vek'lor, Crazed Worshipper and perhaps a Brawl, Gorehowl and Grommash Hellscream.
Warlock - Imp Gangboss, Brann Bronzebeard and Sea Giant for sure. Then you can also add Gormok and then maybe even a Leeroy if you love the SMorc life.
Why you no Rogue?
To cut a long story short, you need either Preparation, certain Legendaries or both to make them work well. If someone wants to take a good crack at Rogue though without using Epic or Legendary quality cards then I'll happily include them into the guide.
/edit: If this is going to be a sticky then this needs to be better. Gonna be busy raiding tomorrow but if I'm not knackered I'll start fleshing things out a little more by doing an individual breakdown for each class rather than having it bundled together with minimal information. If people want to contribute I'm happy to add your lists and suggestions, just need to come up with a much better structure for the guide, should go without saying but and if you contribute then you will be credited.