Where Is the Best Place to Store All of Those Collected Upgrade parts?

I've never had a sim put food away into anything but the refrigerator, @mightysprite, and I use the sticker boxes (cardboard box) a ton.

If you don't usually have your sims actually interact with the boxes to take things out maybe try placing them such that they cannot be interacted with. I use bbmoveobjects to resize and stack them and the like, so I think that's the case with most of the ones I use.