Depending on the project, I have different ways of storing them. I usually have four projects going on at any given time, and I just leave those out on the table. I have a ping pong table, and there is a cutting mat at each quadrant. There's also plenty of room in each section to just leave stuff out. If something has lots of little pieces, like what you're describing, I leave a 15-1/2" square ruler over the top of it to keep it from being disturbed.
If it's something like a BOM (I call those my "interrupters"), I hang the blocks with skirt hangers and put the rest of it in gallon zip-lock bags or large manilla folders with the name of the quilt marked on the outside in permanent marker. Also, I have one of those 12-drawer (shallow drawers) bins where I keep projects when I'm not working on them regularly. I also keep projects I haven't yet started in there.
You kind of have to decide what works for you and modify it as you go. My ping pong table used to get kind of a mess because things would get shoved to the middle. But I got a couple of wire shelf things that you use to make more space in a cupboard so that the materials for one project could be kept separate from another. Baskets (cheap at Goodwill) are also a good bet, especially those with a handle.
Don't expect to get it right the first time you try, but if you get a good basic layout going, you can add, subtract, or modify as you go. Eventually, you'll have something that works pretty well.
I'm not a terribly neat housekeeper in general (clean, but not neat), but I've always kept a neat workspace. I can't stand working in clutter.