There are two challenges associated with a lower income. One, it can be hard to get a down payment together while also paying rent. However, your state housing authority may be able to hook you up with DPA (down payment assistance) programs.
The second issue is income. People with low-to-moderate incomes may be eligible for HomeReady, a home loan with discounted mortgage insurance, no added fees for the low down payment, and great low rates. Probably your best bet if you qualify.
In rural areas, USDA loans let you buy with nothing down. And if your income is very low, you may even get a subsidized "direct" USDA loan from the government.
FHA programs have pretty flexible underwriting, but the mortgage insurance can be expensive.
Finally, if you're at least 62 and have a sizable down payment, you could buy witha reverse mortgage and make no monthly mortgage payment.