Keep smaller dog-walking supplies together in a clear bin or small basket. Hang leashes and harnesses on hooks near the door you use for walks, on a wall or on the back of a closet door. The best location is the one that lets you grab everything on the way out and put it back immediately when you return.
Start with what you already own and how often you use it. Edit first, then choose a home for each category and buy additional storage only if there is a genuine gap.
My final check is practical: can you find what you need quickly, put it back just as easily, and see when the space is getting full? If not, simplify the categories or move the storage closer to where you use it. An organizing system should make life easier, not become another chore.
Mr. Organized's Answer