The idea behind stands is that you don't have the speakers interacting with the material on a bookshelf. In other words, the bookshelf can be a resonator, and that's what you don't want.
If you get a good pair of heavy speaker stands there shouldn't be any risk of tipping, even on a carpeted floor. I have a pair of metal speaker stands that can be filled with sand if desired. This is to dampen as much unwanted resonance as possible. The stands also have three cleats, I guess you'd call them, which serve a couple purposes: one, to hold the stands in place in carpeting well, and also to minimize the surface contact with the floor.
The advice you've been given about speaker placement is good. The reason for placing them away from the wall is again to minimize the interaction of the sound from the speakers with the wall. Bass can build up if they are too close.
I have two pairs of monitors, one large and one small. To get the sound stereo sound balanced properly I've taken a great deal of care to make sure that the speaker positions are well matched on the right and left. To the point that I carefully measured their placement with a tape measure, both from side to side and from front to back. The angle of each speaker is also carefully matched. I even put a little indicator on my computer monitor showing me where the exact of the stereo image is, so when I want to be sure of panning I put my nose in line with the indicator. Sounds silly, but the detailed measurements have really made a difference. Especially with two sets of monitors, as you don't want the stereo image moving around when you switch monitors.