Your idea of plastic baggies (with zip-lock seal?) is a good one!
When I cut out a pattern, I label every group of squares, triangles, rectangle, sashing, borders, bindings, etc. with # and size on post-it notes AND pin that note to each group of cuts, so it does NOT come off!
For storage, I use large pizza boxes (re-use) but to be sure there is no grease distribution to my good fabric, I line it with freezer paper; then label the box and they can stack neatly.
I guess to get real anal, one could "date" the day the project started and organize it chronologically? Naahhhhhhh.....
However, I am getting better... no new projects started until these -several- are finished. LOL
Good luck.