The most common material you’ll find in most tack shops is stainless steel. You may see a variety of other materials, but the majority of bits in your local shop are likely to be stainless steel.
Stainless steel has a neutral taste and is very durable. The core alloy in the steel may contain nickel, but the stainless steel coating should protect your horse from nickel exposure if that’s something of concern to you.
Stainless steel doesn’t encourage salivation in any particular way, so if your horse already tends to excessive salivation this may be a better choice. The cost and durability are also a perk.