You do want ammonia, nitrite at zero to make sure that you are at the end of your first part of the nitrogen cycle, but it is way more complex than this. When your tank gets stable for coral, then your focus shifts...
Like all sugars and building blocks in life, you need some, but too many can be a problem. You need ammonia to give coral nitrogen since most cannot use nitrate directly without expending a good amount of energy to convert - don't go with the mob on here who think that higher N levels are coral food. If you have too much ammonia, then fish gills can rot and things can suffer. ...so you want to test near zero ammonia on a test kit (even though most of them are junk), but feed your fish a lot so that they are always producing waste. Nitrate is not easily used by most SPS (we are in the SPS forum) and the energy needed would be bad for SPS on the brink or not thriving.
Same is kinda true with P, except it is more complex. P comes in many forms... organic, inorganic, phosphate, phosphorous... your test kit will test for one kind but fish waste will be several different kinds and nobody really know what is more efficient for corals to use. In the end, you need a trace of P.
Heavy import and heavy export... feed the fish a lot to keep lots of available N and P and then export a bunch to keep residual N and P levels relatively low. Availability > residual. People can test for residual, but the results are fools gold. I only test to make sure that I have a trace and also that they are not climbing.