Each mortgage lender (LendingTree is just one example) will scrutinize your financial background—such as your debt-to-income ratio and assets—and use this info to determine whether to loan you money, and what size monthly payment you can realistically afford. This will help you target homes in your price range. And that's good, because a purchase price that's beyond your financial reach will make you sweat your mortgage payment and puts you at risk of defaulting on your loan.
Typically, purchase offers are contingent on a home inspection of the property to check for signs of structural damage or things that may need fixing. Your real estate agent usually will help you arrange to have this inspection conducted within a few days of your offer being accepted by the seller. This contingency protects you by giving you a chance to renegotiate your offer or withdraw it without penalty if the inspection reveals significant material damage.
Outside of these Fannie Mae, FHA, VA and USDA loan types, there are state and local assistance programs that can help you get into a home with a low-down payment. There are also towns that offer incentives to move there, ranging from student loan forgiveness to free lots of land to build on. Even though these programs don’t cover your down payment for you, they can help you save money elsewhere if you can come up with the initial down payment up front.