FHA technically allows a credit score down to 500, however, FHA doesn't lend the money directly, they just insure a portion of the loan to protect the lender.
So for this reason most lenders set their minimum credit score requirement at 640 these days, although I have seen lenders who can go down to 600.
According to FHA guidelines, if your middle credit score is below 580 then you don't qualify for the minimum down payment (3.5%) - you would need to put down 10% at least.
With regards to the scores that you get, those are not "mortgage" credit scores. They are just consumer scores which are different. Mortgage lenders pull their own type of credit report that gives a greater weight to things such as mortgages and installment debt, which are greater predictors of how you will act if they grant you a mortgage.
You may find a lender out there who is willing to give you a loan, but if they are the only game in town then you are probably going to pay more for your loan. you would be much better served working on your credit and saving money for a few months and re-visiting things then.
That's just one humble loan officer's opinion. Hope it helps and best of luck!