Way back in the dim and distant past before I moved here, my Clarkson Tool & Cutter Grinder enjoyed it's own corner of the workshop, with peg boards on the wall to safely store the various grades and shapes of stones - and this is my preferred method of storing them.
On moving they were all safely wrapped in newspaper (dated July 2007 !!!!) packed into boxes and the boxes temporarily stored next to the machine. This arrangement persisted for far too long - best part of a year ago I bought some suitable dowelling to make peg boards, but then it dawned on me that I'd run out of wall to mount them
So rummaging for the right stone for a particular job became rather haphazard resulting in many partially unwrapped boxes sitting on my layout table and getting in the way - something HAD to be done.
I had a five drawer wheeled tool box left over from sorting a pile of CNC lathe soft jaws (tool box proved too weak and wobbly!) - it was bent back into shape - each drawer was already lined with firm foam - so I started unpacking the stones into the drawers so at least I could see what I had.
I don't like storing them like this, but so long as the tool box isn't wheeled around violently they should survive.