You are being told various things because not all lenders have the same requirements for getting a mortgage. Some require a certain credit score, some require collections, charge-offs, repo's to be paid off if there is a balance owing no matter when it occurred, etc.
When credit scores aren't so excellent (such as a 636) & with a low down payment, usually FHA financing is the better loan program because interest rates are pretty low compared to the alternative option which is conventional financing, plus FHA doesn't require collections, charge-offs or repo's to be paid off as part of the loan approval (although each lender is free to make their own requirements for those items to be paid off, which are called "overlay guidelines"). Not all FHA lenders require owing charge-offs, collections & repo's to be paid off though. FHA financing also can accept people with a credit score as low as 500, but anything below a 580 credit score requires a 10% down payment (otherwise with a 580+ credit score FHA is OK with a 3.5% down payment). Again, however, lenders can make their own credit score requirements as long as they aren't any less restrictive than FHA's are, i.e. a lender could decide they will require a 620 or 640 credit score for their FHA programs.
Conventional financing typically requires just a 620 credit score (Fannie Mae & Freddie Mac programs always need a 620 score), but it is tougher to qualify for and while collections, charge-offs & repo's aren't required to be paid off, it's more common for lenders to have those overlay guidelines that will require them to be paid if the accumulated balance is over a certain amount. With less than 20% down conventional financing typically needs higher credit scores (660-680) because then private mortgage insurance (PMI) is needed and the PMI companies can impose their own credit score & qualifying requirements as well, although it is possible to obtain PMI with just a 620 credit score through a company called Radian, but not all lenders utilize that PMI company.
Because buying a home is something that should be taken very seriously, and your situation is a little more complicated than someone who has excellent credit, make sure that whoever you apply for mortgage with has thoroughly reviewed your entire situation before making a decision to use them for your financing. I'd even recommend you have an underwriter (the person who ultimately decides if you are approved or not) review your situation prior to making an offer on a home, as if paying off that repo is not possible then you'll want to make sure the underwriter isn't going to require you pay that as part of the loan approval.
Shane Milne | Lending in all 50 states | NMLS #81195
shane@thebesthomeloans | 949-273-4161 direct