Also, forgive me the egregious typo in the questions which, thanks to copy/paste, appears twice. Embarrassing.
How do your organize a current/active research project?
How do your organize a non-current/inactive research project?
How did you figure out what filing method works for you?
In my case, it took me years of experimentation to find out that I really do think best in small, managed piles for active projects, and the best way to store these is in a paper sorter, and that that's okay. (Midway through graduate school, I finally realized this.) My current one is falling apart. The case was robust, but the cardboard wasn't strong enough to support so much weight at that height. Thus it is that I'm considering how to fix or replace it right now, and why the whole problem of paper organization is on my mind. The small cardboard ones (no more than about three shelves high) can be remarkably robust. I may replace it with bookshelves with lots of extra shelves. This, however, is rather tempting.
For inactive projects, I can put it all away in binders for easy reference. The binders fit in nicely on bookshelves - whenever there's enough space spare!