Well, having done some of this before, carefully consider your lighting. Sure, a plain, two-lamp 4' fluorescent surface-mount fixture will suffice, it won't necessarily be pleasant. Also, a centered ceiling fixture will cast your shadow on the walls, which can be less good. At the same time, you really don't want recessed can lights punching holes through the ceiling you just redid in fire-resistant wallboard, either. So, my vote is for cove lighting, which you can array around the room. Fixtures and lamps can be pricey to simple, too. Making a "drop" to create the cove alos gives you a place to add recessed fixtures, if the room dimensions warrant, too.
Now, on the walls, one of the spiffiest answers is to use slotboard. And, it's worthwhile to spend a bit more to get the store fixture grade slotboard too, if only for getting prefinished material, or a range of color choices in melamine-faced.
The slot board is a nice solid material on the wall, you screw it in inside the slots making it nearly no-visible-fasteners. The store fixture people have a huge range of hangers and brackets. But, regular peg-board fixtures work just as well (and sometimes better, using tool-grip PVC dip on the brackets). There are also storage bins in various sizes to go on slotboard as well.
If you are near to a middling-large-enough town, there's usually a plastic nameplate engraver who already has stock handy with a bend to seat in the slots, if a person were of a mind to label their collection on the wall.
The other nice thing about slot board is that you can rearrange things as your collection grows or changes.
OP's 5x5 room will be a little small for the ideal thing to have, a comfy chair in the middle of the room.
I always specify a good sized exhaust fan for these rooms. Which is nice if one is using cleaning solvents. But rather better if one is contemplating one's collection with an adult libation and a cigar (which is why a comfy chair is handy).
Rug over the floor is better than carpet. Tile (VCT, ceramic, quarry, etc.), wood (planked, parquet, engineered) are really more to individual esthetic and budget.
Oh, and in-swing doors are better than outswing, as that protects the hinge pins. If outswing is unavoidable, then for sure get pinned hinges.