Handle props on stage the way you'd handle a line of dialogue or bit of stage combat, with intention and awareness of the four dimensional stage picture; the audience is tracking that prop; where it ends up and how it gets there is as important as how it was revealed and used. If a prop is dropped in a rush, or without intention, we in the audience smell b.s. In general, I think props are most effective when they're handled 'with ceremony,' a bit more slowly and self-consciously than in 'real' life--just as you slow down stage combat a bit--so that it reads; I don't mean go overboard--slow motion is silly--but the moves matter. This is easiest to see, for me, when handling drinking alcohol on stage; alcohol is always a story.
The same care with props goes also for managing the sound of footfalls on a stage when actors' shoes make a noise, either by design or (more commonly) accidentally (usually in a small or black box theater with cheap or loose stage flooring). If the sound is unavoidable, it has to be choreographed, at least to some extent, otherwise actors literally step on their own lines.
Thanks. I needed to get that off of my chest--bad prop and shoe choreography has been on my mind for a couple of years