For the smaller items like shells you could use boxes like this, it is divided into compartments and although designed to lie flat it will stand on the side. This one is 23x16 cm
The company I got these from isn't showing them on their website but may still be available elsewhere. It's clear acrylic and sold for beads & model making.
(Also cutlery trays make quite good display 'cabinets' stood on the side)
No idea what you do with feathers tho - those sticky pads that museums use to secure valuable objects might work attached to the quill.