The alloy that should be used depends on the application. If the mesh is going to be subjected to harsh conditions that introduce corrosive substances, 316 should be applied.
This is because the molybdenum that is added to 316 stainless steel wire mesh, allows it to withstand more corrosive applications.
If you are simply using it to sift non-corrosive materials, such as food particles or aggregates, then a 304 stainless steel mesh will get the job done.