I think you get some gold or packs for beating expert practice mode with each class. Other than that, just do the daily quests. If you are inclined to spend a little money, the Naxx adventure pack yields a bunch of good cards. Some competitive decks are fairly cheap - face or midrange hunter, warlock zoo, and mech mage come to mind.
Mage is a decent class to play as their common class cards are pretty good (frostbolt, fireball, water elemental, polymorph, flamestrike). And, yes, warrior armor will stack if you aren't taking face damage.
Edit: Feel free to add me, Taho#1438, if you want.