Rustling leaves...I like the idea of that. Its fairly difficult to come up with generic background noises that are calming at the same time. Leaves sound like a good bet though.
I think its fairly dependent on the climate you grew up in. e.g. I'm from a fairly warm/dry climate so "storm" sounds mean rain & relief from heat. Plus the local farmers are much happier (except when there is hail involved).
>damage the building you are in
Again - never occurred to me. Its just a non-issue here. Buildings are built to last & we don't get natural disasters here.
Sufficiently strong weather and uncontrolled fires could put you at risk, but the extremely vast majority of my experience with these sounds has been with the safe varieties -- I don't think I'd find it as calming otherwise.