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I would get the CUC with your first fish, then you can add the corals and other fish whenever you want, as long as you don't add too many too fast. The harder corals to keep should be added later, since the water parameters are more stable.
Fish, CUC, then easy corals like leathers or mushrooms first. If that goes well, try a LPS like a Frogspawn. When you have to cut those corals back because they are outgrowing your tank, then consider SPS corals.