What kind of floppies?
There's a lot of advice out there, to sum up from memory: store up-right to keep pressure off the media, store in the same kind-of environment you live in, avoid temperature extremes, avoid too moist and too arid environments. The longevity of the media will greatly depend upon the quality of manufacture.
Addressing the cardboard box, I don't see that as a problem so long as it's sturdy and prevents distortion of the disks. I use some Sterilite plastic storage boxes you can get at some dollar stores, grocery stores, or I get most of mine from Target.
I tried using CD storage (The Container Store has some nice media cases which accommodate CD, VHS, and DVD) but 5-1/4s are not quite the right size. I do not know of much which is designed around the 3-1/2 disk size.
