Crown is the convex edge, always place up when you do joists, beams, rafters etc so downward weight force will tend to make the member straight, rather than sag.
So it like counteracts any future sag, rather than ADDING to sag.
Not all boards have crown, most do, and some minimal and some alot more.
When you go to yard and pick your beam, find one w a bit of crown... Common in a 2x6x12 maybe like 1/4" - 5/16 or so.
For your purpose it would be better than a straight one.
Putting loose wood shelves in a bookcase, you put any warped arched sides up, and put your heaviest books on that .
And you could always double up/ laminate two slightly crowned 2x6's... not as strong as a single 2x12, but better than single2x6.
Marc