Also, is it legal to deny the person base on criminal history? 

In other words, are certain providers less expensive, have a faster reponse time, provide more comprehensive reports (i.e. criminal background in addition to credit checks), etc.?

Frequently check your court websites to see if he gets any criminal charges.  

When I add a tenant  I do a criminal  back ground check at very  the least .

I check 4 main areas: credit report, court records (criminal & evictions), income, and land lord references.I don't look for a specific credit score.  

If an uninterrupted chain of documentable residence cannot be established for the previous 24 months, this is unacceptable.A criminal background check will be done on all applicants and any occupant 18 years of age or older.

As both a short and long term rental owner I’ll just add a few words of caution here...AirBnB and other vacation rental sites like HomeAway are great for the purpose they originated: short term rentals, but they offer minimal protection for the concerns of many owners needing to secure their properties for longer lease terms.As a traditional property manager I’m far more interested in ensuring I pull a full criminal background check, speak with a potential tenant’s present and prior landlord, confirm consistent employment/income sources for > 6 months, and ensure a potential tenant has a track record of paying other bills they have agreed to in writing like credit cards, car loans, and others.On the contrary, at best AirBnB/HomeAway/others give me the following info on guest/tenant: a blurry selfie (that could be their dog)confirmation of a non-specific government IDconfirmation of an email address I can’t seecurrent city/state of residencelist of reviews by individuals running a different AirBnB (that I have no way of confirming is not the guest’s best friend)Property insurance secured by (and in the interest of) someone who is not meWhile I’m OK with taking a gamble on unknown guests using my property for short term stays, stays of longer than 1 month generally involve: Someone looking to move significant belongings in with them (that I cannot legally remove in most states)Moving in for a period of time they’re generally unable to pay for entirely upfrontTenants receiving access only after a legally-executed lease, criminal, background, credit, and income check that’s par for the course in a professional, term stay arrangementEven beyond the blatant lack of risk mitigation tactics common in long term lease agreements, the fact remains that many STR platforms are also skimming 10-20% of gross revenue off the top of owners’ profits for little beyond the initial SEO and payment processing.

The problem with them is the limited number of apartments available compared to those who need them, and the violent criminal element using these places as homes between prison sentences making them dangerous to other who live there.So there are solutions, just not perfect solutions.Good Luck!  

I had been charging $45, then paying a screening company $29.45 for the criminal/credit/ eviction portion. 

Take photo from at least two different angles so I can see every section of fence, all trees, etc.Exterior photo of all four sides of the home.