1) Treat all prospective tenants EXACTLY the same. EXACTLY. Not mostly the same. EXACTLY.
2) Taken in order of application, accept the first one that qualifies.
Anything else leaves you open to charges of discrimination. And, frankly, it's the fair thing to do. \
If I were doing the checking myself, I would be loathe the cash the 2nd applicant's check until I knew I had rejected the first one.