Masks go into my mask box/pouch, tilting the top and fronside towards the edge so the skirt doesn't bend. Straps get pushed cleanly into the mask itself, no folds or bends other than at the sides.
Fin sideways-length wise or flat in my Rubbermaid 24Gal Action Packer, as does everything else including my mask box. Action packer gets stored in my garage, kept away from car fumes. Outside my parents house, my house doesn't have cars going in and out of the garage, so it's just sitting on a shelf away from moisture, sunlight, and heat.
Any extra pieces of gear also go in a rubbermaid box.
BC's get hung up on hangers, same with wetsuits.
Everything is dry, dry as can be before storing. Even the insides of my booties. If they aren't they get placed in my bedroom floor, to dry out with the help of some night time body heat.