My self I like the "master test set" from Aquarium Pharmaceuticals(A.P.). It has everything you need to test while trying to establish the nitrogen cycle. I like it because the cost is reasonable, the color charts are easier to distinguish (IMO), it lasts up to 3 years. It claims on the bottles that it is only accurate after a year, but i think that is more of a precaution. If you close the bottles tightly, and store them in a cool dry spot they should last. As far as copper water supply plumbing killing fish, it is only possible if the water is very acidic and the plumbing is very, very old or the pipe is somehow leeching copper into the supply. If you suspect a problem with copper in your water supply then get a test kit for it. A.P. has one as do other brands. Since you have a watersoftener I suspect you have hard water so a GH/KH test wouldn't be a bad idea, though not necessary. If you have a bypass on the softener it is probably better to use non-softened water. The salt used to recharge the water softener also goes into your supply. Too much salt over a long period of time is proven harmful to aquarium fish. Potassium chloride is probably the way to go or by-pass the softener. Do you have a sediment filter before the water softener? If you do try to go to a 1 micron filter and see if it helps. I am not sure of the product used in rust removing in softener salts. I think it is some type of cleating agent, but I am not sure. Anyway research this to see if the rust removing ingredient is safe for aquarium fish.

An iron test may be a good idea. <.3ppm is considered safe drinking water. i think reccomended for aquariums. also a filter may help clear the polishing filters come with micron or use d.e. earth>

A small reverse osmosis unit will solve your problem, use 90% RO water and 10 % regular water when you fill up the tank and refill evaporated water with RO water, that will keep the mineral content in safe levels. Copper piping doesn´t leach enough copper to make it unsafe for the fish but invertabrates are the ones that do not tolerate copper.