Get one strong enough to remove the paint/stains (borrow or rent). 

On the walkthrough, the home looked great other than some rotting siding, a couple broken windows, stained carpet and old water stains on kitchen ceiling.

been through this so many times, tried everything, dark colored granit is probably best (light colors stain) but expensive.

In my case my wife designed the house with cararra marble counters, farmhouse sink, etc which are prone to staining and scratching. 

Leave the basics. do a detailed inventory for your stuff like an excel sheet with # and condition ( no scratches, stains, burns).

Any holes/dents in sheetrock, particularly where doorknobs hit after the tenants have broken off the door stops.Excessive dirt at the corners of walls where people put their hands in order to turn corners.Dirt and grease on stove and oven.Dirt, grease and scum on tub and shower tile.Built up crud, hard water in toiletsUnkept lawn and shrubsCuts and tears in any linoleum or carpet.Stains in carpet.Smoke stains on ceilingsGrease on range hood.Dirty windows.CobwebsDirty baseboardsCrap left in garage.Unauthorized repainting of walls.These were always the big ones, and hardest for them to dispute, for me.all cash

The bathtub in my rental unit is stained from some smart *** burning documents in it, so I have these brown/yellowish burn stains, does anyone know how I can go about fixing this without changing the tub or installing some kind of liner?

I find a stain that will match as close as possible and go through each room covering the scratches.

Rented immediately for $600/mth, ie. 12% nominal yield after painting to remove the smoke staining, and some kitchen repair.

An inspection of the structure would be in order, untreated water damage can lead to a variety of problems, including staining, warpage, deterioation of pressboard(cabinets and shelving), mold, termites and other critters.Water is broken up into three categories when determining the effects on a structure, and what is needed to be done.