J.L.
I store mine in tall shot glasses on my bathroom counter.
I clean them with a gentle shampoo, and it just depends on how often I use the brush. I rarely use my lipstick brush because I only put lipstick on for special occasions. So I clean it after each use or else it sits there and gets gunked up. Things like my concealer and foundation brushes (which are used daily) are every week, sometimes a week and a half.
ETA: when I store them, the brush side is up...not down in the shot glass. =)