There is a spot, in the toilet bowl, right underneath where the water sits, that is a bunch of brown scratches. This is a new apartment unit I'm moving in. If I just remove a few inches of water, I should be able to paint over it, so it doesn't look like there is some poop stains. What's the right way to go about this? What type of paint? What is the right way to remove enough water so that I can paint that spot under the sitting water?
Here's a trick we used to use on old houses that we renovated many years ago. You have to be very careful, but if you get a flexible razor blade (the typical kind), you can lightly scrape the hard water and other deposits off of the inside of the bowl. You have to go slow and with a light touch so as to not scratch the porcelain, but for some really bad toilets, this is the only thing we found that will work. Bend the razor blade as you work so that it conforms to the roundness of the bowl and try to just get the edge of the blade under the deposits but over the porcelain. You might end up with some faint silver scratch marks, but these are superficial and are from the blade not the bowl. They will come off with regular cleaner.
Turn off the toilet shut off valve and flush the toilet. The water will go out and the toilet won't be able to fill up. Let it dry and get some acrylic appliance paint and paint the area. Matching the paint could be a challenge unless it's white.
If this is a rental, get with the landlord and have him fix it or at least get their OK to do the work.
Painting is likely to make it look worse and you'd need a paint that essentially needs to deal with flowing water and standing water. There's also a chance your landlord might now be happy about it, so documenting the current condition and getting their permission first is a good idea.
What you really need is an strain remover that's acidic - the stuff we use says "solvents, acid, surfactants" as its contents and comes in a brown plastic bottle. I just dump maybe a cup or two in, scrub it hard and leave it for about 10 minutes, and flush. Repeat until clean. It takes time (and this can mean, every day for a week, just keep at it till its clean or there's no difference)
Vinegar (the white, slightly nasty synthetic stuff) might work, but the brown bottle stuff smells better.