What Are The Ideal Chemical Levels In A Freshwater Aquarium?

A little out of order:
NO2 (and ammonia which you don’t mention) = 0 You’ll only get these values once the tank has cycled. If you use fish to cycle your tank, do water changes to keep the levels below 0.5 ppm until they stay below this on their own.
NO3 – preferably below 40 ppm
The others will depend on the fish you keep. African cichlids prefer hard, alkaline water while Amazon river fish are naturally adapted to soft, acidic water.
But, since most tropical fish species are bred in captivity now, those you buy in fish stores tend to be fairly adaptable to conditions found in most public water supplies. That’s not to say there aren’t some (like the cichlids) which require you to add a rift lake salt mix to raise the pH and hardness.
Use this link to find the tolerance range for most of the common aquarium fish: http://www.fishprofiles.com/profiles/ It also helps when keeping fish to choose ones with similar water chemistry preferences.
However, it’s not advisable to try to do too much adjusting to your water chemistry – the more you alter the normal chemistry, the more chemicals you have to add to your tank each time you do a water changes (and anything added should be added to water in a bucket outside your tank). It’s best to find fish compatible with the water you have, then no adjustments will be needed except for regular water changes (with the addition of a conditioner to remove chlorine/chloramine) to lower ammonia, nitrite, and nitrate.