As an area real estate broker, I can tell you that there are a lot of 3 bedroom homes on the sales market in LeRoy. Frankly, "realtor.com" is one of the best websites that tends to list MOST real estate for sale in NYS. (Individual companies which are members of the local MLS but have their own websites with extensive listings, are paying money to advertise other company's listings.)
If I were looking to rent a home on the market in LeRoy, I would have to CALL THE AGENT/company who has a SIGN ON THE PROPERTY and who is IN FACT the listing company. Then I would have to present myself pretty highly, because typically as part of a "sale" the house is in "as-is" condition (and rumors lead many Owners to believe that having a tenant increases the chances of having a property be harmed or damaged by that tenant.)
As you can see this is a very time consuming job and one which you may want to hire a licensed agent/broker to do "on your behalf" as a Tenant's Agent (that means they would represent you not the owner.) I did this once deliberately by holding a "tenant's open house" when the seller needed to make a monthly mortgage payment. About 25 people were there, so I had to advise (representing the owner) that any tenant willing to "rent until purchase closing" would be given preference as the seller really wanted to sell. So the tenant rented for awhile then we had the closing. This reasonably protected the Seller. So, even though you are speaking about renting, it may still very highly be in YOUR interest to go to a bank, see if you may qualify to "purchase", and so on.