Here's how I store them:
I used this Ikea off-white drawer to store most of my punches.
Just a bunch of papershaper punches.
SU and McGill punches
I love the EK Label punches and I used them mostly for sentiments for my card projects.
A drawer of EK XL Large and regular punches
Another drawer for my EK punches
Then another drawer that has my Fiskars hand squeeze punches.
Fiskars edge punches
MS Punches including deep edge punches.
Another bunch of MS punches
Drawer that has all the seasonal MS edge punches.
Last drawer has the original MS edge punches, which is really hard to store.
Got a couple of this Ikea rod, mounted it under my Making Memories Embellishment Center and used it to store my MS craft punches and corner punches.