Shellac based primer - yes. Brands are B.I.N, Zinzer, Kilz, etc.
Thats if you are going to paint. I think that's what you will want to do. I had the same siding on my old house. I did a clear finish on it and a color matched putty on the nail holes. When painting the recommended procedure, as I understand it, is to use Stainless nails set flush. Your installer used a nail gun with pressure too high which recessed the nails. If you have recessed nails I would putty over them, prime the putty and then paint. Bondo would work well. If the nail is flush, consider using a nail set to push it below the surface and then putty/bondo.
Yea, lots of work.
As for paint - I really like Benjamin Moore. Ask them for recomendations on prime or not over their solid stain. May only need to spot prime your nail treatment. Ask them to be sure.