This is currently how I keep my watercolor brushes clean. I have a silicone kitchen "sponge" that I got really cheap. I didn't like it for my kitchen, but it's great for watercolor. It fits in this long, rectangular plastic tub which I use because I can keep the water level low. The tan/brown cup is where I keep my fresh water. I can reshape the bristles on it. When I'm done, I dry them on the black brush rack, which I bought for my makeup brushes several years ago (and then quite wearing when the pandemic hit). It's not great quality. You have to keep the weight balances so that you don't cause it tip over and I've cracked both of the plastic pieces that keep it standing (taped it back together). But was cheap and it works so there's so that.

One thing I used to do with my makeup brushes was use rubber bands or hair ties to tie my brushes to my towel rack with the bristles down. It works and you can be sure that your brushes are safe, even if you don't have a brush stand.

 

As far as storage goes, it depends on how nice a brush is. Fancy brushes live in a wooden box and the rest in a jar or a plastic bin. To be honest, I don't like my wooden box because it takes up too much space while also not offering a lot of space for brushes. In fact, it nearly ruined one of my rigger brushes. I guess the brush slid forward and came o rest on the bristles, which go severely bent out of shape. I was able to reshape it with warm water, though.

 

I really hate it when my brushes get full of dust. I find it's really difficult to get all the dust out, and it takes up time where I could be painting. I haven't been able to solve that problem yet.