Which is most likely to cause irregular bleeding, the mini pill, the skyla iud, or the nexplanon implant?

All of them can: You have listed 3 Progesterone only methods. Irregular bleeding is a common side effects of any Progesterone only method. One can not predict ahead of time who will have this issue and who will not. I don't think we can accurately rank these methods in terms of potential bleeding issues. Mirena (levonorgestrel) (which you did not mention) rarely has breakthrough bleeding.