Vertical is definitely the way to go, but you still have to move them around occasionally so they don't set in any 1 position for to long. I've had bamboo, steel, fiberglass, E-glass, Composite, and graphite rods.
Bamboo can warp in under a week if not handled properly. The bamboo that I have is antique quality and they live in wood cases with silk over cedar shaving lining. The cases stand in a closet safe and are rotated weekly, the rods are shifted within the cases twice yearly besides their once a year fishing trip.
Steel can be tempermental too. I am guilty of warping 1 of 3 Heddon Pals by leaving a wood Injured Minnow hooked to the Cast-Rite reel I'd put on it and left with tension on the line for 3 weeks. Not to mention coroding the reel by not drying the linen line on it. SHAME on me!
I've been given 2 fiberglass and 1 low-grade composite rods that were badly warped by spending years leaning 2-3' to a corner of a garage. They are un-usable.
I have yet to see an E-glass rod that was warped but I'm sure it can be done. As for Graphite I've seen 2 that were warped to the point that their tips were 2-3" from where they should be.
If your going to store rods Horizontal make sure that their whole length is well supported. If your going to go verticle make sure that they're standing as close to vert as possible.

Tight lines,
Wade