Know which kind of stain you have
Whitening works on some discoloration and not on others, and knowing which you have saves both money and disappointment. Extrinsic stains sit on the enamel surface, from coffee, tea, red wine and tobacco, and these respond well to whitening. Intrinsic discoloration comes from inside the tooth, through aging, trauma or certain medications, and it barely shifts no matter what you use.
It is also worth knowing that peroxide is what actually whitens. Products without it polish rather than bleach, which helps surface stains but goes no further. Higher concentrations work faster and cause more sensitivity, which is usually temporary. And no whitening product changes the color of crowns, veneers or fillings, so those can end up mismatched. The reviews below cover strips, kits and toothpastes with that distinction made clear.