The mortgage you obtain will be based on the lessor of the purchase price or appraised value. If you purchase the house and all its furnishings for full price, and if that full price is the same as or less than the value, then your mortgage will be based on the purchase price. If, however, the house appraises for less than the purchase price, then the mortgage will be based on the appraised value.
The amount you have to put down is based on the mortgage program you select and the location of the property. For example, if the house is located in a Declining Market Area, you may have to put at least 10% down whereas you need to put only 3.5% down on an FHA mortgage (assuming of course the mortgage amount is within the limits for the county in which the property is located).