Usually, the first offense results in a cease and desist order.

We use a 1-5 scale for various key things that are important to us: rental history, income, debt to income ratio, referrals, clean car (it shows how they'll take care of your property), criminal check and credit check.  

Also checking their criminal background is also a vital step.

In the ad it's self I would just simply say that "we do an in-depth criminal and reference check (must have good references!)."

If this post is offensive to anyone, I apologize up front. 

Before you start marketing your property, write out a clear list of qualifications (income, credit, criminal, evictions, etc).

We typically like to meet your pets at some point in the process, too.Our tenants’ safety and the peaceful enjoyment of their home is important to us, so we do a credit/criminal background check on all applicants aged 18+.

However, doesn't look like any violent offenses - so I'll be able to get rid of her without her trying to kill me.

This is not meant to be offensive but based on the paragraph above you are nowhere near being ready to do this deal alone. 

Then the prospect should pay an application fee for criminal record and credit).