Many first time home buyers use and FHA loan (though any buyer can go FHA if desired) because they only require a 3.5% downpayment. The MHDC program through Missouri will grant a buyer 3% of the 3.5% downpayment that is needed, as long as you qualify - there are tight income restrictions. Your lender can help you navigate the best programs. I can give you a referral if you need someone.
It is also common for buyers to add a little but to their purchase offer and request that the seller give them a closing cost credit. This will help offset your cash output needed to close on a house. If you have any other questions, I am happy to help you with the process.