The opposing council will either file a criminal or civil suit.

I check credit, court, criminal background, terrorist and rental history.

I've had two occasions where the reference they listed told me not to rent to them because they were violent, late payers, or too needy.Not doing a criminal, credit, background check, which might have revealed criminal or credit problemsBeing slow to evict (mentioned by others)Believing their sob storiesAccepting partial paymentsFailing to document every conversation or interactionNot walking through the property to make sure they're taking care of it (I now walk through every 9 months so I can see problems in different seasons)We've found crack pipes and other paraphernalia after they moved outWe've discovered piles and piles of trash (some bagged, some not) in closets, basements, sheds when trash cans and pickup service are included in their rent - all they had to do was carry it out, at no cost to themWe've Found smokers, pets, extra peopleOverall, I've had great success as a property investor. 

With luck, you can get someone out if there's a significant criminal charge. 

Regarding criminal checks that’s concerning and I read on another thread that we can still run background check that includes credit, etc.

We use an income requirement (3x rent), plus look at criminal and eviction background history and it serves us pretty well.  

If you offer WiFi, you could buy a ROKU TV on black Friday or cyber Monday (I'm seeing REALLY Netflix account (or upgrade your own Netflix to a family plan that costs $15 per month). 

If I were you, I would pre-screen people before showing them your property (i.e. ask them qualifying questions like "will you pass a comprehensive screening [credit/criminal/evictions]?").

Two questions:1) How should I check credit and criminal background (Service or Trusted Website)?

I think we're all hoping nothing criminal has occurred but it may be safer to let anyone know so they can take precautions