The first thing I'm asking myself these days is why do I wish to keep something. I've found a lovely person here who takes my cutting scraps as I have decided to no longer keep anything smaller than 6.5" square. You don't need to keep them at all, you can bundle them up and donate or otherwise pass them on and that's perfectly ok.
Mostly I used plastic bags with whatever seems best, keeping like with like. I use a sharpie to write the dimensions on the outside of the bag. So if you have subunits of the 4-patches completed, I'd keep them together. If they are 2-units or I call them dominoes, those would go in a bag. Likewise all the same sized strips go together by size, not color.
When you get a bunch of them you put them in a bigger bag/container or figure out what to do with them. You can decide to go full scrappy and put together whatever you have that finishes 3" or your desired size, whether that is a square, HST, or 9-patch.
I get baggies in different sizes at the dollar store, starting with sandwich bags, and then maybe I'll group a particular set of scraps in a gallon bag. The clear zippered bags that things like mattress pads come in are nice for larger groups.
Plastic bags slip around so you do need to keep them in a drawer or box. If you don't store them well or have easy access to them you are not likely to use them which defeats the purpose of keeping them in the first place.