I would have thought the marketing would take place before the tenants moved out to minimize the time the house is vacant.Are there standard items that are typically done (besides a deep cleaning of the property) during a turnover? 

The stain is the dark area on the countertop and we have tried many cleaners and hired a cleaning company to try and remove it, but no luck.

After refinancing, you get a free property and cash flow minimally.

Much of the information on this site is about how to obtain rental property while minimizing the amount of your own personal cash you invest in it, however they key word there is "minimize".

Is there a good way to approach this process to minimize blow back?

So I can afford very very minimal down payments. 

They’re TAW and have been for years, so upgrades have been minor and minimal during that time.

Life has changed a lot since this law was passed, but in those dark ages, people would not buy a house if the person was known to have had AIDS.  

I’m probably looking for something on the lower end of the scale since my use is minimal.

Almost like a shot in the dark, you never know where it will land.