picking among qualified tenants without legal liability?

[Johann Jells]

I am planning an open house and expect a number of qualified applicants, there was lots of interest (apparently the rent is STILL too low!).  My question is that if I take a number of applications from qualified tenants, am I under any obligations, chronological or whatever, or can I simply pick the one I think will be the best fit?  I just don't want anyone saying something like "my credit and income are perfect, you've discriminated against me!!"

Usually I show by appointment, and prioritize by first application, or at least pretend to, so I can say, "sorry, we just need to run the credit for someone who wants it, if they don't work out I'll call you."