I use Zinsser BIN shellac primer. Three or four coats sanded smooth between.
For dark purple, I'd then put down a couple coats of black sanding flat then put the purple down in thin coats.
When it was the color I wanted I'd then clear over it. Sand it flat then wax it till it glows.
I'm a little obsessive about sanding stuff flat, ok, mad dog crazy. But I like a mirror finish.
For satin use satin clear and maybe don't wax it the 20 coats of wax that I use.