When I did screenings,  I did the usual credit/civil/criminal background check,  verified income,  interviewed prior landlord (almost nobody seems to actually do that - at least none of my former tenants have ever resulted in a new prospective landlord calling me)  and for anything less than perfect I asked some combination of  2nd months rent,  co-signer,  or increased security deposit.   

Fees charged for EACH new tenant on a one-time basis: $300 PER PET, $80 pet "dna" fee, $25 criminal background.

The tenant will be facing criminal charges and the landlord civil.

Obviously, a criminal background check and a landlord reference but what else am I overlooking? 

Arkansas, Its a criminal  to stay in the house after the eviction!

We run credit and criminal history on everyone.

So I use a service where when the tenants fills out an application and pays it runs a full background check the main things I look at is credit and criminal history.

There's nothing much you can do to screen the tenant as far as criminal background or eviction history.

I would create a short one page application to be filled out whenever new adults are moving in, and the company would provide you that and a nominal fee ($10, $20, how much do criminal checks cost in your area?)

All you need is a company to do the credit and criminal background search.