I do not currently pull a credit report, but am considering doing so in the future because it will help better screen and tell me if there are options for financing the home rather than rent credit if I choose to go that route. Perhaps Greg can share which credit service he uses and the cost.
I've just been at his a little over a year and am continually refining my process but what I have found so far is the following:
Big down payments make a difference. Having tenants pony up some serious up front dough aligns both of your interests. On a home I have $6-$10K invested in I usually get $2000-$2500 down which equates to 25%-40% approx.
They must have good landlord references, and it can't be mom and dad. You have to call and verify. If they start saying that they had problems with the landlord it's a red flag and will usually disqualify them. I have found most landlords to be friendly and willing to tell their experience with the tenant.
Verify their income. I make them text me a picture of their most recent pay stub and the prior year W-2 or last pay stub for that year. That will verify that they are indeed employed and what the earnings actually are. People will lie to you so verify.
Run an evictions and criminal background report. If there is a criminal issue from a couple of decades ago and it wasn't violent then I may give them a pass. But if they recently got out of prison for drug dealing, then no way.
Job Stability. I do look for someone that can hold a job and not bounce around a lot. I can't tell you how many say they don't have a job but they will get one at Amazon next week.
I don't use my real name on this forum as I work as a GM for a large mobile home retailer which has it's own financing division. They have the best performing loans in the business which in part has to do with them being an "equity based" lender which means the worse the credit is, they higher the down payment is going to be. This makes it tougher for the buyer to walk away and if they do, it increases the recovery rate for the asset.
Don't think in terms of first months rent and deposit. Think in terms of 20%, 30%, and 40% down. Also if they have the capability of paying all cash for a house, then those will be the best payers. Those are the only ones I will make an exception on regarding the landlord references and many times will get a parent to sign a lease since that is where the money is usually coming from anyway.