A few months back, I had a client that went 3.5% FHA with a CHDAP (California Homebuyer's Downpayment Assistance Program) silent second loan of 3%. The seller credited my buyer 3% for closing costs (which is roughly the amount of a typical closing). So my client came in with about .5% (of purchase price) of his own money. This is one option, but it isn't zero out-of-pocket.
Are you or your wife a Veteran of the military so you can qualify for the VA loan? My client just closed on a home with a VA loan. That would be a great route if you have access to it. But, the first step is to speak with a lender so you know if you currently qualify to get a loan, and you'll be given steps to get you qualified if you're not. I have great lender that takes a consultative approach (Chad Cockerell from Guild Mortgage). But, feel free to contact me to discuss your financial situation and your home purchase goals.
Here is a good link to look at:
Link to a good lender:
Another option is a FHA 3.5 percent down payment program which will allow you to receive gift funds if anyone in your family will consider helping you purchase your first home.
Once you have a loan program selected and a preeapproval, that is the best time to stop your home search and it would be my pleasure to help you.