The best way to keep Reels is in their original boxes,some reels comes with cloth bags.
Make sure they are clean & dry before storing,if by some chance they are accidentally given a glide you have to disassemble, clean and remove the old grease.
Dry your Rods ,store them in the Rod Socks & original tubes.
You can carry your small gear in a Tackle Bag,as you usually set up Rods,Reels before Fishing & carry them as a unit,however some people set up on the storage I found it was difficult especially when fishing in the night as stuff can be left & sometimes lost.

Note: Carry the gear you need in fishing.