The minimum down payment for a conventional loan is 3%. However with a conventional loan, the more money you put down, the better is going to be.
When you put up to 10 % down on a conventional loan, the terms of the loan could be better than an FHA loan.
Whether FHA or conventional, if you are putting less than 20%, you will have to pay mortgage insurance or private mortgage insurance.
But with conventional loans, as soon as you reach the 20 % equity the mortgage insurance can be removed.
Whereas with FHA loans, you have to continue the mortgage insurance till the life of the loan.
Hence many people refinance their mortgage and get a conventional loan once they know that they have 20% or more equity in their house.