Currently the only base character left is the Skinner. There are also three new characters which have been released on the kickstarter recently, the child thing, the water bearer and the news. Not sure what mooshy's thoughts are on people picking them.
Indeed, those classes are all on this PDF at the very bottom, so they're available for players to choose. I've already demonstrated a willingness and ability to handle a huge party, so I welcome anyone who cares to create a good character. This is a big world in the Twin Cities Wasteland, there's room for all sorts of weirdo folks.
I second that question