The best scenario for the buyer buying subject to is to have enough money and good enough credit to qualify for a new loan at current rates should the due on sale clause be invoked by the lender  

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

It will likely still continue being a difficulty.You mentioned bills, are they credit card bills?

Most non-FHA loans will require at least 15% down but you'll have to have amazing credit.

Any local bank that does this kind of financing should be able to approve you as long as you have a good enough credit score and never declared BK.

@Stefano Vrolijk it all depends on your credit history, whether you have an SSN/ ITIN and how much you can put down.

And when you said the management company takes a 550 credit score , all I see in your future are evictions .   

I require a high credit score 680+ and two prior landlord references.

They could even hire you to do the work on the house and instead of paying you they could just give you a credit at closing.

Rate will be highly dependent on loan size, credit score, LTV, location, and property type, as well as a few other factors.