Paying Off Debt vs Saving

We have about $16k in debt (credit cards, car, etc) and we can't take out any equity loans.. so we'll have to raise the money to adopt ourselves. My question is.. do you think it's better to pay off our debt and take out an adoption loan after (we may not qualify since our credit rating will still show some late payments and whatnot), or put whatever extra we earn into savings for the adoption fees? If we save the money and don't pay off our debt, will the debt count against us? Our joint income is about $75k, and we're a family of four. Thanks! -Rachel