Oh, this is what I absolutely enjoy about League.
You never pay for power. Champions and runes are available through IP, which you get from the game in general - even if you lose a game, you still get IP, upon whereas you can use it to buy champions.
Champions are different prices, but all are available to you WITHOUT paying real money. The only thing that actually costs real money in the game are skins, which "decorate" your champion, and trust me, people pay a load for that. But otherwise, no, they don't sell you power for money. It's pretty awesome.
And there are levels in the game, but it hardly affects your gameplay. It's more skill rather than level - a level 1 CAN outplay a 30 (though it will be hard from lack of runes and masteries), the only difference between levels are masteries, number of runes, and whether or not you can play ranked games. It's a really balanced game.