Ideally you want 0ppm ammonia, 0ppm nitrite, and less than 20ppm nitrate. You want nitrates as close to 0ppm as possible but under 20ppm is considered safe for long term health.
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What is the GH (general hardness), KH (carbonate hardness) and pH of your water supply?
This information can usually be obtained from your water supply company's website (Water Analysis Report) or by telephoning them. If they can't help you, take a glass full of tap water to the local pet shop and get them to test it for you. Write the results down (in numbers) when they do the tests. And ask them what the results are in (eg: ppm, dGH, or something else).
Depending on what the GH of your water is, will determine what fish you should keep.
Angelfish, discus, most tetras, most barbs, Bettas, gouramis, rasbora, Corydoras and small species of suckermouth catfish all occur in soft water (GH below 150ppm) and a pH below 7.0.
Common livebearers (guppies, platies, swordtails, mollies), most rainbowfish and goldfish occur in medium hard water with a GH around 200-250ppm and a pH above 7.0.
If you have very hard water (GH above 300ppm) then look at African Rift Lake cichlids, or use distilled or reverse osmosis water to reduce the GH and keep fishes from softer water.