There are a few ways your down payment can impact the loan process.
For example, if you make a small down payment, you’ll need to qualify for mortgage insurance on an FHA or conventional loan. You should avoid conventional loans if you have a low down payment and credit score; further, PMI premiums are tied to your credit scores, while FHA mortgage insurance premiums aren’t.
Mortgage insurance protects your lender against losses if you default, and is added to your monthly payment, loan amount or both. You can avoid private mortgage insurance with a 20% down payment on a conventional loan, but you're stuck with FHA mortgage insurance regardless of your down payment.