At a bare minimum, new tanks need regular checking of NH3/4, NO2, NO3, pH and SG. Unless problems arise during the "new" phase such as impossible to beat algae or pH swings, other tests probably won't tell you much. Kits like GH and KH would be mainly diagnostic at that point. Established tanks need mostly NO3, pH, and SG checked periodically, usually before regular WCs. SG may need more frequent testing on smaller tanks. Other tests will vary by stocking and how desperately you want to know the levels of various things. Phosphate testing is a good diagnostic for algae problems and is useful when keeping phosphate-sensitive animals (e.g. stoney corals), but in established tanks it might always read zero and thereby become a bit pointless if there's a lot of desirable algal growth in the tank/sump. From my experience, additional kits are either mainly diagnostic or for keeping tabs on dosing of various things in more complicated or specialized systems (calc, iodine, etc.).