I won't give you the "build your credit" speech, other than to say if you did then you would have options.
There are a very few options out there for credit scores as low as 500, but the catch is that they are so risky to the lender that they require a really high rate of interest and a huge down payment- like 30% down. If you're on that strict of a budget then I'm guessing you don't have a 30% down payment just sitting around. So while yes, there are a few lenders that will work with a 500 credit score, the options aren't great or even attainable for most buyers. So in a case like that, what's better - paying a huge down payment to get a 9% or 10% mortgage, or just renting?
FHA requires a 580 credit score and 3.5% down payment (although not many lenders will go below 620) and Conventional financing requires a 620 credit score and 3-5% down. So you are not there yet.
I'd advise you to rent within your means until your finances/credit are in order to buy. Owning a home is not a basic right, it is a privilege, and it's not throwing money away on rent if you can't qualify for a loan. So work on making yourself able to qualify for a loan. It's not easy, but if you can set a gameplan and follow directions to a tee then owning a home will turn from a dream to a possibility. I work with plenty of buyers that come to me in rough shape but are willing to work at it.
I hope this feedback helps!