effective methods to get more cards from chests!?

I have been loosing a lot to people using goblin barrel, spells, prince, spawner decks and baby dragon. And what really sucks is I don't have those cards. I don't plan to invest any money to buy magical chests. Currently I'm in the barbarian bowl and I don't think that the chest systems really helps you to progress evenly in the game. If you are lucky you get good cards, if not you're done! I have the following questions:

1. How do I get these cards through the chests?
2. Is there some way to get more cards from the free chest.
3. Any suggestion for best deck? I'm a level 5.