Down payment minimums are a function of the loan type used. FHA requires a minimum of 3.5% down. VA and USDA require 0% down. Conventional loans range from 5-10-15-20% down. You can always put more down to reduce the loan amount and thus your payments each month.
If you are asking about earnest money then that is negotiable between you and the seller. Your agent will have an idea of what is customary in your area. If you want to offer an amount with $500 earnest money and the seller wants you to put more in escrow, they will counter your offer with that amount. Your Realtor will be better able to advise you on earnest money than the lender will. The lender will be able to tell you more about money as a down payment to the loan.