An FHA loan is an insured loan, insured by the Federal Government. A conventional loan is investor funded. The property must meet minimum requirements to be eligible for FHA financing. Most do. Just because the listing agent didn't put it in the listing, doesn't mean you can't use FHA. But , I would ask before you fall in love. No there is no pre approved list. The home just has to meet minimum standards, in other words it must be habitable. The inspection isn't that rigorous as in the past. Now keep in mind that the inspection you are talking about is done to provide the lender with value, not habitability. If you purchase a home that is existing, I can not stress strongly enough how important it is for you the buyer to purchase a whole house inspection. This is vital. Write any offer "contingent upon an inspection". That way should the property have issues that could cost you a great deal of money to repair, you can renegotiate the contract or walk away.