There is no climbing or league advancement. You simply choose the bracket appropriate to your collection level. If you try to play in champ with level 1 cards, you won't find any playable cards. If you try to play in silver or gold with max level cards, you'll just see them capped like you currently do in brawls or tournaments. This was designed explicitly to prevent the people getting beat down with max decks in bronze or people with bigger collections getting stuck in lower leagues. It's essentially 'choose your own adventure.'