Hello Saradjine, and thank you for your question.
It looks like you have two questions here. One is how to find the best house you can afford, and the other, I believe, is how to minimize or eliminate your out-of-pocket costs. I am going to give you the short version here, with links to articles that provide more in-depth information.
First, the best house must be affordable. And it appears that affordability is a concern for you. So I am going to list a few programs that people with income challenges use to buy homes.
1. If you wish to buy in an area considered "rural" by the US government, which means not in a large city, you may qualify for a 100 percent USDA home loan. If your income is moderate-to-low, you get the loan from a USDA-approved lender. If your income is low-to-very-low, you may get your loan directly from the federal government, at a subsidized interest rate as low as 1 percent. Here is more information about how to get a USDA loan here: https://themortgagereports.com/34135/what-is-a-usda-loan-eligibility-rates-advantages-and-downsides-for-2018
2. There are other ways home buyers minimize their out-of-pocket costs. The VA offers eligible military and former military members and families zero-down financing with no mortgage insurance and great low interest rates. Here's a comprehensive guide to VA home loans: https://themortgagereports.com/29182/va-financial-benefits
3. Did you know that according to at least one study, 90 percent of homes in the US are eligible for some form of down payment assistance? Down payment assistance, or DPA, is either a grant, which doesn't need to be repaid, or a loan, which may not have to be repaid if you keep the home long enough. At The Mortgage Reports, we have put together a complete guide to down payment assistance. note that in many cases your income can be pretty high and you may still qualify. https://themortgagereports.com/33553/complete-guide-to-down-payment-assistance-in-the-usa
4. For people who work as first responders or teachers can purchase homes with just $100 down through the Good Neighbor Next Door program. And buyers get a 50 percent discount on the homes. A 50 PERCENT DISCOUNT ON THE HOMES. The 50 percent off homes are foreclosure properties that had FHA mortgages on them, or homes located in "revitalization" areas. Find out more with this article: https://themortgagereports.com/13751/hud-good-neighbor-next-door-program-sells-u-s-homes-for-50-off
5. Next, some buyers reduce their out-of-pocket costs by asking the home seller to pay them. Instead of negotiating a lower price, these buyers ask the seller to pay the closing costs. Another option is having your lender pay the closing costs for you. Of course, the lender would lose money on that unless you pay a higher interest rate. But it does save you out-of-pocket costs. Here's an article about seller-paid costs: https://themortgagereports.com/29154/get-sellers-pay-closing-costs-to-pay-your-closing-costs
and here is one about lender-paid costs: https://themortgagereports.com/20695/no-closing-cost-mortgage-low-rates
Please write back if you have more questions. Good luck with your house hunt!