I was a licensed lenders for many years. Before the crash, we had some basic matrixes for the B & C lenders that indicated credit scores, DTI, LTV, employment status etc. Since these companies are all out of business, we have Fannie Mae, Freddie Mac, and FHA to rely on. Their matrixes are possible to get, but there are so many exceptions and alternative options, overlays and variables, you shouldn't try to do this on your own.
It's not just credit scores and ratios. Talk to a great local mortgage lender and discuss your situation. They can advise you on the fastest steps you can take to qualify, or improve your situation to get a better rate.