Ions like manganese and iron are likely to be apparent to anyone drinking the water when they're present in excess.
Ions like nitrate and phosphorus are not typically problematic in brewing and may not be worthwhile testing for.
The heavy metals might be a worry if you're on your own water source but those WILL NOT be a problem in the US if you're on a municipal water source.
Testing for silica may be a good idea if you are in a desert area where that ion can tend to concentrate, but it's not typically a problem in other parts of the world.
Zinc is typically present in most water at very low concentration and the testing method might not be sensitive enough to pick it up, so it might not be worth testing for. Confirm with Ward that they can detect to between 0.1 mg/l (aka: 100 ppb) and 0.5 mg/l, since that's the minimum and maximum zinc you want in your water.