When things get fishy and you are not sure that the offer you are so into is legitimate, there is one hard, fast, unbreakable rule: DO NOT PAY ANY MONEY!

Secondly, feel free to pester.  Let the potential landlord know you are uncomfortable with this situation.  Do not rest until you get a working phone number and address to reach the person, not to mention the verifiable address of the rental property.

If it is at all possible, acquire the services of a broker to act as a go between.  He or she will be able to ascertain whether this rental offer is legitimate, and it will save you from getting duped into anything.

Keep other properties in mind.  Sure, I am in love with this house, it suits all my needs, and it is affordable, but I know I logically have to realize that there are other places available out there.  I cannot hang all my hopes on this one property; I simply have to hope it turns out well.