Bathroom shelving used to mean one sad piece of frosted glass propped on two plastic brackets above the sink, the kind that came with the apartment and held exactly a toothbrush cup and regret. That has changed for the better. Open shelving has gotten sturdier, the hardware has caught up, and there are real options now for small bathrooms that used to just have a cabinet and a prayer.
A shallow shelf over the toilet suits almost any bathroom, rented or owned, because that strip of wall is usually dead space anyway, and it is the first place to put one if you have nothing. Wider, deeper shelving works better near a tub or over a double vanity where you actually need to land towels and bottles without them toppling. Humid, low light bathrooms do better with sealed wood, metal, or stone rather than raw wood, which will cup and swell on you no matter how much you want it not to. Think about the room's temperature swings too, a bathroom that gets properly steamy in winter and bone dry when the window's open in summer is hard on any material that isn't finished well.
When you're buying one, check the fixings before anything else. Look at what it actually screws into, and whether it comes with the right anchors for your wall, because a shelf that works in drywall will fall right out of plaster or tile backer if you use the wrong hardware. Run a hand across the edge for rough spots, press down in the middle to see if it flexes, and check the brackets sit flush against the wall rather than wobbling on contact, because that wobble only gets worse once it's loaded with glass bottles.
Over time, wood will darken a touch from steam even when it's sealed, which is normal and fine, but watch the underside and the wall mount for any softening or dark spotting, that's moisture getting in where it shouldn't. Wipe it down weekly rather than letting splash marks dry into the finish, and every few months pull everything off and check the screws are still tight, because steam loosens things faster than you'd expect.
If you're starting from nothing, go with one solid shelf over the sink or toilet before you think about a whole system, it does the most work for the least wall space and the least commitment.
I'd start in a warm oak or a simple white painted finish, something that won't fight with tile that's already there.