I store A4 colour, A5 colour etc in clear plastic folders kept flat in Iris Cart drawers. A3 papers are kept in an art portfolio, speciality papers such as vellums, gold card, are stored separately. I have one or two A4 plastic boxes but they are just too tight a fit and you can damage the papers lifting them out, so use them for current projects and finished cards. All bits and bobs of offcuts are stored by colour families in clear plastic folders in a ring binder[ haven't enough Iris cart drawers or would use them!]
I find storing by colour is the easiest way.
HTH
Judy C