I've grabbed a screen shot of the BP rental calculator, and using whatever information I could find on the listing, and through the broker, this feels good.  

Can anyone recommend a tenant screening service that does a good job with a national criminal background check?

my screen is all messed up.

Thanks for the comment about putting them both on the lease, I'll go that route if they pass the rest of the screening.

As long as you use your clear and strict screening criteria to eliminate applicants in the end you will have only one that is the best.

I just finished screening, and doing a background check on potential renters. which I went thru trans-unions (smart-move) website. 

Tenant screening is also important.  

What are your recommendations for a company that has screening and management capabilities (specifically rent collection and income and expense reporting).

As I am screening applicants, one of the applicants has low credit score (500+), no bankruptcies, no evictions but has late payments.a) Tenant is willing to put down 1.5 month security deposit (state allowed maximum) and 4 months of rent in advance.

I'm sure the snarks on here will say the best tenant proofing is good screening before you rent  :) I personally like tile floors...I have given up on wood...laminate and carpet...provide extra air filters for the AC unit (unless you use replacing them as a reason to go by and check out the place every few months) fire extinguisher in the kitchen...make sure smoke detectors are installed and working properly ...if it is a single family be sure the tenants know where and how to shut the water off ...