That's a pretty good explanation of how the levelling system works but you're just missing one thing:

Your total collection power determines the league you can play in (bronze/ silver etc) - and you need to buy or rent cards to get your collection power up.

Legendaries give you relatively more collelction power, so do Beta's compared to reward cards for example. And gold cards give you more too.

It is a bewildering system to get your head around!