@Matt Smith I think the most important thing you need to do here is evaluate what your criteria are, and why. Knowing why helps when making decisions so you understand how to evaluate borderline cases. Some of the criteria used by people matter more in Class A and less in Class B,C or D. Some always matter. As others have said, look at the property type, the best tenants you are likely to get, and go from there. But it is also important for many reasons to set firm, unyielding criteria. Why? Well two very good reasons. Bending the rules usually means "settling" for something less out of desperation. Bad move, it also means problems more times than not. The other important reason has to do with discrimination laws. You need to be able to show that you accepted/rejected tenants based on consistent factors. Otherwise you are opening yourself up to criticism and possibly losing a lawsuit. A few important things to consider:
Does credit score really matter? Personally I think it only does when you get into the really low numbers. If they have no evictions and a few years of rentals they probably are typical in considering shelter the priority, even if they stretch their income a bit thin.
Do evictions matter? If so do you allow an exception after x years?
Do convictions matter? What kind get no exceptions? What kind get exceptions after x years? Personally violent crimes and sex offenders are generally lifetime no for me. Exceptions that I would make - sex offenders who were 18-19 and got charged with statutory rape with an over 16 yr. old ... after 5-6 yrs. without incidence.
Income ratio: Evaluate and set it and make zero exceptions, or expect to regret it. Unless of course you accept Section 8.
I suggest you require payment of deposit upon signing, first month rent before they get keys. Again, no exceptions. Depending on state and local laws, find out if you might be able word the lease so that deposit is not refundable if they bail, but you do not need to do an eviction. Not all states allow that kind of thing but if they do, get it in your contract.
Always include all adults living at the property on the lease. Always require that all of them meet the requirements. Always make sure your lease says that they are all responsible, together and separately, for compliance with all terms of the lease. Otherwise if the "responsible one" moves, you are left with someone less than acceptable as a tenant.