So I figured, why not hang them up?
I found this really great multi-use hanger from Ikea that only cost me 8 bucks, then I attached old shower curtain rings to it to hang my jewelry from.
And voila! All my necklaces and bracelets easily accessible and on display.
However, if you live somewhere with a humid climate, it might be better to store your silver jewelry and valuables in a way that will prevent them from becoming tarnished. Perhaps like this.