I wasn't trying to be a know-it-all. It was a sincere question. You put "first fixed" as the title, which suggested that you were getting your first fixed-gear bike. Great. I love them. Then your post talks about a coaster brake. These two things are incompatible, which is why I asked. It may be that you don't want a coaster brake at all but really want to have a fixed-gear bike, but we can't tell.
Maybe you should read
this.