On the exterior, anything concrete I would pressure wash and then stain a light gray and seal.  

So I cleaned them, changed the hinges and handles and sanded the stains out of the laminate counters.

It was really dated and need some love, there was a water stain on the ceiling which scared people away, it need carpet, paint, bathrooms and kitchen were dated but nothing major.

I was hoping to see if someone had stained them and what they used.

It has cosmetic issues that don't look alarming (Paint scratches and stained carpet).

Both bathrooms had stained blue carpeting in them.

It makes it water/stain resistant. 

From what I can see in those pictures that is just smoke stain, not structural damage.

Louis in the south city area, everything is old so there isn't much to really set your-self apart and the 2 bed up the street will rent for the same price as the one your in no matter if it has a painted wood stair and newer front door vs. the stained wood stair and original front door. 

All brick with stone lentils and sills with tons of leaded and stained glasswork.