An FHA is going to be your best bet with a low credit score like that. But your score better be at least 580 or above, because "about" 580 won't cut it. The lowest any lenders I have heard of will go is 580 and that is a hard cut off point.
The large down payment will help your case, but in addition to the credit score they are going to take a very close look at the "why" behind those low scores. Your recent credit history - the last 6-12 months - probably has to be clean and they will require all judgments to be paid off and probably any collection accounts as well.
Our company personally requires a 600 credit score, but there are a handful of lenders out there who can do 580. I'm sure some of them are here on this site.
Best of luck!