S.D.
I would pay off your credit card debt first. I'm not sure what info you found about consolidation, but it may affect your credit. Are you going through a company for the consolidation or are you going to put it all on one credit card?
If you do want to save some, put a good chunk towards the credit card debt and see if you can get a lower interest rate credit card and consolidate the remaining debt. I would also pay off the credit cards with the highest interest rates.
Ultimately paying off all the credit card debt first would be the best idea, but having an emergency fund is important too.
I can totally relate to your situation. I was in a huge amount of credit card debt, but finally worked with a financial advisor and he helped us tremendously. If you want to discuss further let me know.