There are many ways to progress in Splinterlands but in the beginning the most important is DEC you receive for battle wins. Quest rewards are limited 1 chest per day until you progress into Silver league. And one chest gives you a random reward so you can earn about 10 card per month and should not pretend that cards will be Epic or Legendary. Common and Rare reward cards will not progress you much.
Howhever, DEC earnings are predictable and you do not requred to advance in league progress to earn more. The progress depends only on you rating, not collection power. Moreover, the DEC reward for each battle win is based on the square of current rating. You will earn 100x more DEC on rating 1000 comparing rating 100.
Here is official DEC release announcement:
High rated players are much more powerful than lower rated players, and are therefore able to capture significantly more Dark Energy from the pool after each Ranked battle win. The amount operates on a quadratic curve meaning that a player with double the rating of another player will earn 4X more DEC after each Ranked battle win.
It is vital to progress in rating first to earn more DEC. Then rent/buy cards to progress in collection power and leagues.