That is a quandary I’m sure many artists have to face. I used to paint with acrylic paints on canvas and board and quickly ran out of space to store them! As a teen, unless the painting sold, I basically just started painting over my old work because I had no room left to store new work. (Ugh!)
As for watercolours, they’re mostly done on paper and are thinner, thus easier to store. Those larger-sized “under the bed” plastic totes can come in handy. You can purchase them in most department or big box stores. Of course, there are artist’s bureaus and portfolios made for the purpose, but they can be expensive. If you have an unused chest of drawers, you could use that as well, though of course it depends on how large your paintings are and if they’ll fit.
That issue of where to store my finished paintings is the main reason why I do the majority of my paintings in my watercolour sketchbook. I can scan them in and make prints of them later on if I want to sell them (I rarely sell my originals unless they’re commissioned pieces – just a personal choice)