Hello Leanne, USDA and VA are the way to go for $0 down, please note that any lender fees or prepaids maybe rolled into the loan to lower the expected out of pocket costs. As Shane mentioned you could take advantage of any 1st time home buyer grants and downpayment assistance programs to offset these costs as well. Next possible option is to shop for Assumable VA mortgages, where the current owner of a property wants out or needs out of the mortgage.
If you are buying with cash . Just find a home and make an offer. I reccomend using a real estate agent to help you make the process fast, smooth and easy.
If you need a loan. I would reccommend reaching out to a loan originator and obtaining a Pre-Approval. Make sure they have all documentation needed.
If you need real estate agents or Loan originators contacts I can help 518-526-4964
I would recommend you get your Pre-Approval started and out of the way. A good source for a reputable and fast-moving lender will be a good local Realtor. Once this is out of the way your lender can help you with local Bonds and possibly Federal grants, etc in your area. USDA areas could be one source. Step one is a good Realtor in your market.