I'd also pay them off from lowest to highest. I personally wouldn't cut them up, unless my spending habits were so that using the CCs were an addiction. Otherwise I would pay them off, keep them open, and use once in a blue moon to keep enough activity on them to keep from being closed. Closing them will hold back or even hurt your scores because FICO will ignore the balance and CL of any given CC that you close. That'll keep util high on your other cards and high util overall, and that's the source of the drain.

ETA...and yes, what guiness said.