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

Partner effectively, focus on securing your first deal, and build savings and credit.

They have a good reputation from what I've seen but does anybody have a long-term track record with them in Memphis or Little Rock.

I’m pre approved or have a line of credit in place.  

The cash flow from this property ($1,300 profit after expenses) can also help support your ability to qualify for a refinance.HELOC (Home Equity Line of Credit): Another option to access equity is through a HELOC.

However it could be location,  Common area, size, laundry, tenant qualifications (in rough areas you are not going to get many tenants with unblemished credit), parking, look of surrounding properties, etc.   

The lender wants to run your credit score to determine whether you're Dilcia Morales or not.

You need same day cash typically, no loans, no credit. 

I am looking to refinance an existing HELOC to increase the line of credit.

Sounds like you are on the right track doing research on different markets from the Midwest to Texas.