There's a few different ways to focus on a lower rate such as with house hacking and making the investment your primary residence, requesting a significant closing credit from the sellers for standard rate buy-downs (which I've had great success with recently), or utilizing lenders who offer short term rate lowering solutions such as 2-1 rate buy downs (again, ideally paid for by the sellers).

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

Zillow has an easy application for them to fill out. it come back with a credit score and background info. 

No Bank, Credit Union or Portfolio lender wants to foreclose on any loan if there is a way not to.

@Vijay Singh SambasivamI would suggest speaking to local banks, and credit unions.

Otherwise, if the numbers make sense and your credit is good, it should be easy to find a lender.

Instead, you could explore pulling equity out through a home equity line of credit (HELOC) or a cash-out refinance.

I make sure I screen each potential tenant thoroughly (background and credit checks) and require references.

No social or credit pull needed upfront. 

Private lenders tend to focus more on the value of the asset or project rather than your credit score or financial history.