Besides your credit score the loan is just based on the rent of the property.

Potentially disallowing the use of credit scores and criminal record.

However, if you consistently have hard inquiries on your report and a low credit score, you may be viewed as a risky borrower If you have a good credit score, the effects on your score could be minimal, especially if you've been keeping your balances low.

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

In terms of credit, i'm at a decent score and feel i can get a good loan, but what kind of loan should i get? 

DSCRs are loans that only use the actual or projected rental income (from the appraisal), your credit score and your down payment to qualify. 

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

I'm buying in cash and I have a credit score in the 700's.

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

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