*I have never loaded a round of 357sig to date* (still waiting on bullets)... That said, I can tell you that you definitely need a bullet with a short ogive, usually in a HP or FP configuration, in order for the short neck to have enough bearing surface to grip on the bullet. I have on order Rainier 124gr TC's (plated).
I've sized and primed my first 100 cases... I think of them as mini rifle cases for the mostpart, for sizing purposes. I lubed them and just ran them through the 357sig steel die, and they appear to headspace fine on the case mouth in my barrel.
Others have reported running them through a carbide .40 die first to size the body, and then size the neck in a 357sig die with no lube... I have not tried this method yet.