I store my models in cabinets in my model room, although it is getting now full. I have asked this questions several times in the club newsletter and on this website but no-one seems to want to tell me waht they do with their models.
I am a member of this club and have also started a club here in Germany about 3 years ago. Nothing formal like BWSMC, more a regular meet from some modelbuilders where we sit and discuss model building and share techniques over a cup of coffee at my house.
I have only ever shown my models once and that was at an event in our village where our little club put on a stand at the local spring fair last year. The model scene is very different over here than in UK. Should anyone be interested I would be happy to throw summat together and explain the differences.
I hope that your questions are more or less answered, thank you for asking.