From a fair housing perspective, you should have written tenant evaluation criteria. Then, with your written criteria, you should evaluate complete tenant applications AS YOU RECEIVE THEM IN THE ORDER RECEIVED. If the person who applied meets your written criteria, you should offer them the property. If they opt not to accept the property by declining to timely give you a non-refundable reservation fee or actually sign the lease with a full security deposit and first month's rent THEN AND ONLY THEN should you process the next applicant.
You should not process multiple people and select one subjectively; you're asking for trouble with fair housing when someone claims they were discriminated against.
Offer the property to the first one that applies that meets your written standards for qualification.
