ARN
Mine only took a few days from memory. I rang them and asked for it over the phone after about three days and they gave it to me, and then the letter arrived a few days after that.
You can start your medicals without it though, especially your dame appointment as they will do a few checks and refer you to a number of other places for further testing. You don't really need to have your ARN at that first appointment as they don't send anything back to CASA until all of your other tests are finished anyway (well that's what they told me).