I have never rented to a corporation.In the usual screening process, I try to verify the applicants' employment information and rental history.

Sapiens: A Brief History of Humankind by Yuval Noah Harari is a great read that comes widely recommended by top performers.

Her attention to detail, helpfulness, and professionalism are excellent, and she and her daughter Whitney, who is now our property manager, did everything that we needed done remotely such as meeting painters at the house to get bids, letting workers in for repairs, meeting with the inspector, etc.

Credit report, address history, criminal history and more. the full boat.

I've been a cosigner refusing to sign when a term exposing my daughter and myself to possible excessive hidden costs was in the lease. 

Daughter of the couple who owned the home.

Even if it didn't crash, history shows real estate always bounces back.

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

My issue though is my employment history and proof of income since I am just about to start my steady job and do not have proof of prior income/employment.

If you have a history on those STRs and you do a DSCR Loan, you can use the STR income to calculate the DSCR calculation.