Going back and looking at the credit scores of the borrow on some of my investment I personally wouldn't let them rent property from me.

It may slightly negatively effect you credit score

I'm concerned about the impact that filing a claim would have on my insurance score and premiums for this property and other rentals.

His credit score is 620.

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

I invest in mid to upper-income areas where good credit scores and high earners aren't hard to find. 

Hello,We have tenants that moved to Florida from out of state and didn’t have rental history, jobs, and also a low credit score.  

This is all dependent on your credit score, property type, etc.

Many lenders generally have a 1-year lookback window where things will change as soon as its been 12 full months without a mortgage late (then will essentially no longer be a penalty besides any effect on FICO score)

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?