Are there a lot of homes that allow a rent to own option - the short answer to this question is no. The availability of listings or more accurately homeowners who would give this option is, in my honest opinion, less than 3% of the market inventory.
Rent to own listings are indeed rare but plausible if:
A. You can find a homeowner who's monthly rent will be financially satisfactory to you
B. The purchase price of the home would fall into your affordability range at the time when you are ready to exercise your option purchase. This is a matter that is directly related to your debt to income ratio; credit history, down-payment, pmi - if any - and the property taxes.
Generally, you are required to give a month and a half of security; conduct a home inspection prior to renting/signing of on a RTO rental/sales contract. Plus, if the home is listed by a listing agent for the homeowner, you may have to pay a one month's realty fee - there could be attorney review fees as well since your contract is both rental and RTO.
Where did you want to buy? Depending on the county, I could follow-up and tell you how many listings will entertain this option.
Like Julianne, I recommend the Smart Start down payment Assistance Program and a generous seller's concession if you are capable of buying now - credit wise, but do not have the down payment to do so. I also recommend speaking with a loan officer who can accurate advise you as to your affordability range based on your DTI, Credit History and Income.
Here are two links that might help you with your decision and which route you should go.
Email or call me if you have follow-up questions. I have one RTO client who received a 2 year option to purchase for a house in Edison, NJ. Client rents the property for $2450. There are no overages or escrows - please see my article links for more information on overages and escrows.