FHA dropped their minimum credit score for a 3.5% down payment from 640 to 580. A credit score from 500 to 579 would be eligible too albeit with a 10% DP. Even though FHA insures loans with a FICO of 500, lenders may prescribe their restrictions. In 2018, most FHA loans closed between 600-700. Only 7.5% had a score below 600.
The credit report requirements mandate at least two traditional credit reporting agencies, in the absence of which, the mortgagee might have to underwrite the mortgage. Each credit report must include all the details about the lender, the credit agencies, and the borrower, including details of any defaults or late payments, which could adversely affect your approval. Collections more than $1000 may downgrade the mortgage too. However, medical disputes don't factor in downgrading.
You should check your credit report long before you go house hunting. If it is low, FHA counselors can advise you on improving it. You can find out more by calling 1-800 CALL FHA. Your spouse need not have to be on the report, but lenders may check their reports as well. The alternative is a subprime mortgage but with a higher DP.