k-roll, welcome to the QB. When I first started quilting about 5 years ago, I decided to only purchase fabric as I needed it for a specific project... what you will find is that your scraps will grow automatically with leftover pieces from your projects. I think you are smart to organize them from the get-go, it will promote good scrap habits.
I do not precut my scraps, as Jeanne stated, if you need a larger piece and you've already cut them down, you're stuck. I have sorted my sizes into separate totes and know exactly where to go if I need a certain size. Good luck.