Congratulations on getting married.
You might be surprised how quickly your credit score will rise once you pay off the credit card dept. Combine that with a couple other positive financial actions and you'll climb up. So pay off that "bad" debt.
Now, I'm personally a fan of putting all my usual expenses on a cash back credit card and paying it off every month. Credit cards are a good resource for many reasons. First off I like getting the cash back for something I'd do anyway. I also appreciate the security I get from the credit card. If my card is stolen/fraudulent charges, then I don't have any capital (only that credit amount) tied up during the dispute period. If the same happens to my debit card, then actual money is tied up. It is also easier to just pull out a credit card instead of having to deal with cash...I know some will argue that this ease of use is dangerous due to the potential to spend money that i don't actually have...but rest assured, my social awkwardness far outweighs my urge to spend money when I do make it out of the house.
You have to be honest with yourself though. Will you be able to pay the card off each month? Can you control that spending? If not, then I don't recommend this. This rule is key, because if you pay interest on a credit card you lose. But if this won't be a problem, then use one of your cards (if it offers cash back/rewards of your choosing), and put your usual expenses on it...pay it off...and repeat.
As Fradel said, look up Dave Ramsey. He has several videos on youtube, as well as his books. Also read/listen to Set for Life from Scott Trench here at BP. It will help get your feet firmly planted and on your way.