At first it seems as if the champions are imbalanced.

Then you...realise it's true! But it's OK because there are so many OP champs that it balances out in the game.
I say OP, but really it's just that so many champs cancel out other champs. And they're usually the higher priced ones (with in-game influence points -- cash payment riot points makes them mostly the same price).

Still, you should play until you get a feel for the game. You'll get raped a few times during the learning curve, but from then it's fun to pub stomp some noob ass.