Paying off your credit cards

Is it better to spend a quick hard slog of time and focus on paying everything off your credit cards in the shortest amount of time possible without putting any money aside for savings or rainy days? Or is it better to gradually pay off your credit cards while establishing a savings account and a rainy days account?

I've read a fair amount of personal finance blogs and money articles that advocate both ways. Personally I'm leaning towards option 1, however I worry if by doing this I'm leaving myself open for trouble in the future Say for example if an unforseen expense comes up like a doctors visit or a higher then expected phone bill which leads me to then have to use my credit card to get through.

Hmm... I think now I'm leaning to option 2 instead.

What do you do?