Saxophones are mostly made out of brass, but they can be plated with other metals, painted, or lacquered. Almost all saxophones have a clear lacquer on the surface. A black saxophone gets its color from black nickel plating or paint. Silver is another metal used to plate saxophones.
The metal, black nickel or silver usually (occasionally gold), actually changes the tone of the horn and can give it a bit different characteristic. Flute can be made with a high percentage of silver- and that is usually desirable. On saxophones, silver gives a “brighter” sound while black nickel produces a “darker” sound. Maceo Parker plays a gold plated Selmer Mark VI alto. Probably mostly for visual effect.
My Keilwerth tenor (in photo) is plated with black nickel. Overall I like the sound of the horn. However, the plating is not the biggest factor in how you will sound. The mouthpiece, reed, and ligature among other things are much more important.
When saxophones are painted however, it does not help the sound. There are no acoustic benefits to putting paint on top of the metal. In fact, many saxophone players think it “deadens” the sound. Basically, the paint is for effect and can only hurt your sound. Some players go as far as saying the clear lacquer on most saxophones hurts the sound as well and that as it peels off over time the sound actually improves.
Selmer has even made a line of saxophones which do not have the clear lacquer at all.
The craziest material I heard of for an instrument is the a solid platinum flute. William Kincaid played one, which he bought at auction for $187,000. His critics say that he needs an $187,000 flute to sound good…. but it seems to work for him and apparently he can afford it.