Where you put the ladder is a personal preference. I have mine hung from the roof, out of the way and thus freeing up the wall for shelves & cupboards. It is suspended from 4 hooks like these, 2 at each end.
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I also have a chain and padlock to secure it in place, just in case a thief breaks into the garage and tries to use the ladder for their criminal activities.
Painting the floor is a personal choice also, but unless the existing floor is very dusty I wouldn't bother. If you want to paint it for aesthetics, once is has been painted, it will need repainting from time to time to keep it looking nice. Should there have been any oil spills, or leaks etc., on the existing floor then they are difficult to get rid of completely and the paint won't adhere to them.
If dust rather than aesthetics is your concern, and you simply want to stop the surface creating dust, you could apply concrete sealer instead of paint. It won't chip and flake like paint and would also stop any future spills soaking in.