The original concept of "stash" was left over pieces of fabric. I'm sure that many of us have stashes that are exactly that.... left overs. I've never bought material for that purpose.
I store my stash by colors in plastic bins I bought at a thrift type store. If the piece is less than 4" I put it into another type of box (labeled). I did a "Monet's garden" and a "yin yang w/energy" out of 1.5" (1" finished) squares and as a result I have a lot of unused pieces that size. I put them in a special box (labeled).
When most people start quilting they do bigger pieces, usually blocks, until they feel they have mastered the basics enough to dive into pieces which might use the smaller left overs. About a third of my quilts are artsy fartsy and I find places in them for my stash pieces all the time.
However you decide to build a stash, have fun with it! There is no "right" or "wrong" way to build stashes, or even to most of quilting. But, if you don't enjoy it you won't continue.... so ENJOY!