Our community has eleven elevators. Almost all have brushed stainless steel interiors. They resist most damage well except very sharp metallic gouging. The downside is the daily maintenance to remove fingerprints, handprints, and smudges of all kinds. It requires hours per day from the maintenance staff. It's very akin to cleaning stainless steel appliances.
If the surfaces you want to protect are attractive enough that you don't want to cover them, you might consider affixing quarter inch plexiglas sheeting. It is sturdy, relatively inexpensive, and doesn't require constant cleaning.