At the moment I'm using these H&M handle-less mugs, one for face brushes, one for eye brushes. I would definitely recommend having a look at H&M homeware if you're after storage like this - I picked these up for a steal at £2 each I think. Or maybe they were £1...
Primark is another good place to look, they always have mugs and pots which could be handy for this sort of thing. TK Maxx too.
For my sponge, I use this little glass pot which is actually a candle holder but works really well to pop my sponge in. Also, because its glass, it gets pretty grubby fairly quickly, so it really encourages me to keep it clean.
So yeah, bit of a random post, buuuut...thanks for reading, hope you enjoyed :)