You can buy a home if you get a lender to approve you. There are very few programs that allow people with no savings to buy a home. You should review the Trulia Blog "I have bad credit and no savings. Can I get a home or am I stuck renting?" and if you meet that criteria, talk to a lender who works with sub-prime loans. If you appreciate an answer, please give thumbs up. For the most helpful answer, please say thanks with a best answer click.
You may also benefit greatly by finding one that can educate you best on all availlable mortgage options so you can make the best decision for you and your family.
A competent loan officer can also help you increase your credit score so that you can qualify for better rates and terms of any loan you may wish to pursue.
Blessings upon you...