Well, I tend to use the quantum-dump trick remove the stone from the places I don't want it cluttering, but then choose a particular stone-type to build
all my aboveground walls with (and I usually make a lot of them) and then set up a specialised masonic workshop for this (and other specialised masonic workshops for other stone types) in order to turn it into blocks to make the walls(/floors/fortifications/bridges/roads/whatever) that I'm wanting.
But I usually end up doing something like deciding to turn the obviously copious limestone deposits into the aboveground fortress structure, plan the huge complex, start it, and then find that 90% of the limestone layer is aquifer-ridden. Meanwhile, I've got a few-hundred-thousand stones of
another variety being quantum-dumped out of the latest workings.
In short, hiding is easy. Dump it, and if you never use it
ever again, you can just forget about it. And/or
actually set it to be hidden (which you can do in its original locale, as well, but does mean that invisible rocks might need pushing around when you're setting up an industry in the invisible-rock-ridden cavern).
I think the challenge is what to do
with them. And spending ages trying to get (say) five dozen stone mechanisms of
exactly the same quality (and stone-type) takes up some of my stock (but produces a lot of stone mechanisms of a different quality, and occasionally stone-type when I've not managed to restrict the mechanics-maker to the right stockpiles). I can often eat up specific-type blocks much more quickly than I can produce them in making my above-ground structures. Add to that what Poindexterity has just mentioned, and homogeneous furniture (often with a similar 'identical quality-level' OCDing on my part) and that's basically my sink for these.