Hearthpwn

I feel like Shaman is definitely one of best choices for players that aren't interested in spending loads of time/money into Hearthstone.  Most of the core cards are rare or cheaper, but there are plenty of variations that use Epics ( Doomhammer ) and Legendaries ( Al'Akir the Windlord .) 

Playstyle

 Generally you want to get maximum value out of every single card you have.  Most competitive decks currently have lots of ways to draw loads of cards making it way easier to keep a card advantage.  Shaman is definitely on the lower end of drawing power, but makes up for it with the disgusting value you can get out of the Shaman class cards.  From one mana removal to a hero power that can give you spell damage or taunters, Shaman is not short on tools for board control. Keep the board in your favor without investing too much of your hand and repetitively force bad trades for your opponent.  Generally that's how you play every class but Shaman is pretty simple, at least the free version.  Some variations have some high damage combo plays.

Expensive Cards
 

If you stumble into some dust or cash and have enough for a legendary or two you can change your poverty shaman into a competitive deck way cheaper than most classes variants.  I will be adding links to other decks that use these legendaries at the bottom...once I find the decks.

Al'Akir the Windlord
Bloodmage Thalnos
Doomhammer
Sylvanas Windrunner
Reincarnate
Kel'Thuzad