If the delinquent debt was your husband's sole responsibility per the divorce decree, then an underwriter wouldn't give it as much weight but anything negative on your credit will play into the decision on whether your loan can be approved or not. Further, if the not-so-good credit was from other 12 months ago, that is usually enough time for you to be approved for an FHA, VA, or USDA financing.
Where did you get your scores from though? Are you sure your score is a 600?
Mortgage lenders use FICO scores - as a consumer, other than from a mortgage loan officer, you can only get your FICO score from Equifax & TransUnion from http://www.myfico.com as Experian no longer allows consumers to get their actual FICO score. If you are at a website where you can get all 3 scores, you can be pretty certain that they are not FICO scores but a newer scoring system called Vantage credit scores. Vantage credit scores use a lot of the same information to calculate your score, but it gives different "weight" to different parts of your credit profile, so the credit scores are not the same as your FICO scores. I am not sure why Experian no longer allows consumers to get their FICO score from them, I could only speculate that because consumers are not their clients, creditors are, so that may have played into their decision to prevent consumers from getting it. Whatever the reason, at least you can still get your Equifax & TransUnion FICO scores from that website.
Also, the Cottonwood area is eligible for USDA financing, which is 100% financing/no down payment. The catch is your income has to be within eligibility limits ($60k is) and you need to buy in a rural area (which Cottonwood is, you'd have to go to Prescott or Flagstaff to be in an ineligible area. The interest rates are near 4%, the monthly "mortgage insurance" is cheaper than FHA's, and if the home appraises for higher than the purchase price you can use that different to finance closing costs too - so the program is great for people who don't have a lot of funds to put down. You can read some more about USDA Rural Housing financing at http://eligibility.sc.egov.usda.gov/eligibility/welcomeAction.do
If you'd like a hand figuring out how to qualify and what you can qualify for I'd be happy to help.