You should try Mojang's Scrolls [1] if you like CCG gameplay and deck building, but dislike the pay-to-win aspect or the prerequisite of spending hundreds to thousands of dollars to be competitive.
In Scrolls you can use real money to buy preconstructed decks, custom avatars, and a few randomly selected cards in the store's "Just for You" section, but most of your cards are purchased with in-game gold which you must earn through playing matches.
You can play against computer opponents, and your starting precon is strong enough to regularly beat the easiest CPU deck to earn gold which you can use to buy more cards.
Advice for new players: Don't choose Order as your starting faction (I did and kinda regretted it). Buy scrolls from other players in the trade channel, not the store. And use the price guide at http://trading.scrollsguide.com/ as a starting point to figure out reasonable prices for cards (it's based on parsing prices from trade channel chat).