Quicken Loans and Rocket Mortgage are the two companies most well known for their approval of bad credit for 1st time home buyers. There are a couple others, however. Most companies want a credit score of 600 but some will accept first time home buyers with a credit score of as low as 500. With down payment assistance, you too can be a homeowner, as you will be able to put the 10% down they require. New American Funding would finance a credit score of 500 with a large down payment.
To lower your mortgage rates, or to qualify for the mortgage you want with the down payment you want, you may try Lexington Law to dispute bad claims on your credit report. They will dispute over a few months for a fee, and your credit will be improved. Morgan and Morgan offers a similar service. It will only take a few months to improve your credit. If you want to dispute more than one item a month, you may want to get a special credit specialist like 321 Credit, rated 5 stars on google, or a credit specialist through your mortgage broker. They will ask you for more at once, but resolve the issue faster.
Try reading the rules of acquiring wealth called, "The Richest Man in Babylon." Its a simple story, entertaining, with some simple ideas, including to save 10% - but also "increase thee thy wages."