You definately need some more cards.. Decks are normally made of either Mono-Clan (8 characters from 1 clan) or Half-Clan (4 Characters each from 2 clans). That helps you get your Bonus against your opponents.
As to tournaments, the Exact Winnings Table in the game rules shows how many Battle Points you win in each fight. You want to maximize your Battle Points as much as you can.. Playing lower starred cards that can still win effectively is key to placing high in the Dailies. Key is to play smart, win often, and never stop during that hour. I've had instances when I lost the fight I was in, but still gained 18 points due to the points system. (3 cards at 2* win against 4-5* , lose at the 4th card... Lost the match due to Life Totals.)
But remember, the point you're at now with your cards, you most likely won't place in the top 200. People have a lot of decks that are optimized to win DTs. Aim for getting in the Top 1/3 (eg.. 3000 players, get to 1000) and you'll get a credit for your time. 20 Credits = More cards.