Most of mine tend to in use, but when I'm doing a major fence move I use old plastic feed sacks to collect the posts in to transport them. If I was storing them I would leave them in the bags so easy to pick up again.
Sets of 15 tied tight top and bottom with baler and a baler handle inbetween for carrying, then stacked at the back of my storage area. Any tape is wound back onto the reels and pinned into place so it won't come off.