I would say 起 is the most commonly used one and 次 is the least commonly used one. 桩 sounds a little bit more formal than the other two, and it may be used more frequently in safety signs and legal contexts. But all three are common.
BTW, I think you could put "一起事故", "一桩事故" and "一次事故" in Google and check out the number of results to get a rough idea about how commonly used are day. Not much help on the exact differences between them though.