What Would You Do$?$

You're working with a couple who have some questionable credit issues, limited savings, and a recent change in jobs. Both have full$-$time jobs, but they need a mortgage that is more forgiving of their employment and credit history. They filed for chapter $7$ bankruptcy, and it was discharged $2$ years ago. They now have two new car payments. They know they'll need to pay mortgage insurance because of their credit and are okay with that.

As their MLO, describe what type of loan might suit them best? Also describe what kind of loan should they avoid?

Please explain what you considered in making your choices, such as employment history, credit history, expenses qualifying guidelines, etc.