Not all skin reactions are considered allergic reactions. Most skin discolorations, caused by contact of metal with perspiration and skin, are not seen as allergies, but as a mild reaction of the immune system. When having an allergy one gets itching, redness, swelling, etc..
Nickel & surgical steel - hardener & alloy:
Nickel is an affordable metal that is often used to harden soft metals and to give a silvery luster to the finishings. It is usually found in inexpensive components and jewelry. If you have a sensitive skin, stay away from it. You will carry a nickel allergy with you your whole life, so ask for nickel-free quality products.
Despite the fact that surgical stainless steel or type 316 steel contains about 10 to 14 % nickel, in theory, it causes no allergy to most people. Theoretically, the chemical composition should ensure that no nickel is released and as a consequence this might be a good option for sensitive skins.
Pure copper rarely causes allergies, but because it is a soft metal, it is usually hardened and mixed with other metals. An allergy when wearing copper is often caused by a nickel element. Consequently, it is important to purchase nickel-free copper.
Copper does not react to water, but it does to oxygen, thus creating a green patina or verdigris that may stain the skin. An anti-tarnishing layer is certainly an advantage not to be despised.
Copper alloys - brass, bronze and pewter:
Copper is not only a component of brass and bronze, but can also be found in silver and gold alloys.
Brass is a mixture of copper and zinc, bronze is made of a lot of copper and a little tin, while tin alloy is essentially made of a lot of tin and a little copper (and in a minor extent, a number of other, non-allergic, metals).
In principle, none of these alloys contain nickel and as a consequence are allergy-free. Ask for good quality and prevent allergies.
Beware: German silver, alpaca or nickel silver is a copper alloy containing both zinc and nickel and is therefore not recommended.