The mainspring would be a Elgin 817 or Bestfit JA104 (or a JA105 would do). Of course, if you are not doing the work, then finding a mainspring is the problem of the watchmaker.
Any 16 size case appropriate for 1882 would do. They were not factory cased. You went into the jeweler and chose a movement and a case and the jeweler joined them.
We cannot recommend a watchmaker if we do not know where you are.