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

This is why inspection periods are required.  

If you don't need the cashflow then you could throw it at the loan balance.

Of course, with all things, the answers to all these matters will depend on the circumstances.California tends to have more laws on the books and requirements and restrictions that it can be a good idea to form a CA LLC for out of state property so that you as a CA resident are covered, and to try to have your contracts fall under the purview of CA courts.

Leaving you to move and store their items if required by law, clean and repair, etc etc.

And I generally require a sponsor that has full real estate cycle experience with little to no money lost, low leverage, high skin in the game and reasonable fees and promotes.However, other investors will look at these deals as bad/too boring for them because they are more aggressive and not concerned about the risks of default, refinance, interest rates changing etc.

We need an experienced deal sponsor to meet Fannie Mae requirements as well as net worth and liquidity requirements. 

Create a simple spreadsheet or written list to compare the features of each and identify the ones that align with your requirements.

Having the cash means you can balance a higher amount down to make sure you earn the cash flow you want monthly, but also leave some around for more. 

If they can't do a money transfer directly to your bank, have them send a certified cheque using registered mail and signature required (they could send it to your work if you don't want to use your home address).