The current trend towards having a tank with 0 nitrates and 0 phosphates is overemphasized and has gotten out of hand in my opinion. I have personally suppressed or damaged corals with too clean of a tank.
A nitrate level of 10 and under would be good for the corals you listed. None of them would grow in a 0 nitrate tank.
I asked a few questions of a person with a magnificent SPS tank and one of his answers was to not let phosphates go below .04. Everywhere you read it says to keep levels below .03.
http://www.marinedepot.com/reef-tank-parameters.html
I would also like to stress again my belief that there is a big difference in the nutrient levels in a SPS tank and an LPS tank and a soft coral tank. There are multiple reasons to support this, but the easiest to understand is that they grow in different areas in the ocean for a reason.
I was told by an importer once about some LPS corals, "There's an abundance of them that are easy to get to, close to the city; and, you wouldn't believe how "dirty" the water is." Do you think those corals would fare well in a sterile tank?