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

@Cirilo VillarFHA loans, including the FHA 203k, are for qualified non profits or primary residence owner occupant borrowers.Consider the Fannie Mae Homestyle or Freddie Mac CHOICERenovation loan which is the conventional version of the 203k and investors can use it. 

The other two don't have enough data to generate a score because the tradeline driving the 806 score is only reported to the one bureau.

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

To get an abandoned house - like the ones seen by the score throughout the 05 - up to section 8 standards for only a $20K investment (including taxes, insurance and other carrying costs) seems implausible to me. 

My parents co-signed my first loan and knew that the risk of me not paying my mortgage leading to a loan default would fall on them and impact their credit score so make sure that person(s) are aware of the risk they are taking on so they can decide if they are willing to co-sign or not.   

@Itia Dow depends on a lot of stuff and the best way is to actually get preapproved.But for rough numbers for FHA they will want credit score at least 580 but aim for 620 or higher, debt/income ratio to be under 45%, under 43% is even better.

My recommendation is that you screen tenants using a service which offers the full spectrum of reporting (job history, rental history, income verification, credit score, any adverse items as a part of their full credit history, nationwide criminal background check, terrorist list check, sex offender list check and eviction history).  

I've looked into some local county downpayment assistance programs, I've heard advice about using either private or hard money lenders, I've also been told that it could be possible to use a credit card for the downpayment if I've got a high enough credit score.

Which is the "average" of my active credit lines and is a minor factor in lowering my credit score because that is a "below average age".