Not sure why you are asking and not your step dad but anyway...
with such a mess so recent time is the only sure cure for his score to rise. Any item he is paying on time for: car, cell phone, even cable, will likely report to a credit agency and as he continues to meet his financial obligations on time his score will rise.
Taking on a credit card may show in addition that he can handle that type of debt, but so will just being responsible with his financial life.
Buying a house soon may not be the best plan.