Stainless steel is the ideal cover material for your chimney chase. It does not rust, tarnish or oxidize and will last for years. It is not unusual for manufacturers to give the cover a lifetime guarantee. These covers are more expensive than ones made with other materials but the choice pays for itself in the long run. With covers that don't rust or oxidize, you won't have bleeding onto your vinyl covering on the chimney chase. Buy paintable or pre-coated stainless steel if you want the cover to have a particular look.
Aluminum provides an affordable option in a chimney case cover. This kind of cover does not provide the same durability as a unit made with stainless steel, and can oxidize or corrode over time. This can lead to staining on the vinyl chase cover. However, this is more likely to happen near saltwater or locations with a lot of acid rain. If these conditions don't apply to your area, you can probably use aluminum and have it last for years. Aluminum that has a protective coating is even more durable than plain aluminum.
Galvanized sheet metal is another material often used for chimney chase covers. It is more affordable than stainless steel. Prevent the galvanized metal from rusting by painting it with a protective coating and treating holes for bolts or screws with a sealant. Clean the metal with paint thinner to remove grease, apply a rust inhibitor and paint it with metal paint.
Copper is not a material commonly used for chase covers, but it is available from some manufacturers. Many homeowners enjoy the look of the copper. However, it is more expensive than other products and can be even more expensive than stainless steel. Copper is durable and can come with a protective coating to increase its longevity. Copper can look quite attractive with some vinyl chase covers.