If you keep barware out, arrange the everyday pieces neatly on an attractive tray so the setup looks intentional. For smaller cocktail tools stored in a drawer, use an adjustable compartment organizer so different-size accessories each have a defined place. I own and use this type of adjustable organizer.
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