I have $500k in cash to invest as well as a credit score between 750-800. 

Pleasant but could never score any lots there that made sense.

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

In a recent podcast episode there was talk about certain credit unions now offering mortgages to investors that only require 5% down.

Income 3x monthly rent, credit score >600, no evictions, no violent crimes etc6.

I put a link from Rentredi if anyone is interested to look.My screening criteria is 3x monthly income, Credit Score >600, no Felonies, and I have really be on the fence pets or no pets depending on size etc I need help with the tenant selection1.

I've been educating myself on real estate for the past 3ish weeks or so but I have about 10k worth of credit card debt should I try and pay it all off so I can get my credit score up and have better approval odds for my first investment loan (I would be using my VA loan).

For commercial asset classes, local credit unions can often be an excellent resource for more complicated or unique property types. 

My plan is as follows:Keep stuff in my name so I have more lending options and better rates, including credit unions. 

Had a 790+ credit score and then nothing as we went a few years debt free and cash paid for everything.