Do I pass up the first qualifying tenant?

[Vanessa Hornung]

Hi! My husband and I just posted our house for rent three evenings ago. We will be first-time landlords, so naturally, we're already feeling like we're in over our heads. I created my online listing, and with the fact that my husband was going to be out of town shortly after listing it, included a time for an open house, in a week and a half.  We received an overwhelming response almost immediately. We squeezed in a few private viewings before he had to leave town. The very first viewing was a hit- family of 3, more than sufficient salary, has been in their current rental apartment two and a half years and are ready for a little more space, reliable employment. Credit check revealed excellent credit scores, but also an incredibly high debt-income ratio; otherwise, no delinquencies or criminal background. The issue is that if they technically meet our criteria, how do I handle the other prospective tenants, particularly those who are showing as much interest as they had (and have already given us an application fee, which we've not yet processed credit checks for), and those who responded to my listing saying they were eager for the open house? Obviously, I have concerns about the margin of debt they have, especially since a large portion is unsecured debt. I want to be fair, and give everyone their chance to see our home. I realize I am probably being too nice. Someone just tell me the grown-up thing to do! Thanks!