I bought this "Brush Box" a while back and have been quite happy with it. It's large enough to hold plenty of brushes (and also forces me to not just "collect" brushes and really only store the ones I use on a regular basis), is super sturdy, and allows them to remain horizontal when stored.
This case is a popular option: https://www.amazon.com/ArtBin-Brush-Inserts-Translucent-KW903/dp/B000GJ76SE