The main things to test for are ammonia and nitrite since a level of either of these above zero is dangerous for the fish.
Nitrate is only dangerous at levels in excess of 100, but it is good practice to stop the level exceeding the amount in your tap water plus 20, just before a water change. The lowest you can get nitrate by water changes alone is the same as your tap water, and it will go up between one water change and the next. It can be lower if you have a lot of live plants (think jungle) or use RO water or one of the expensive ways of pre-treating the water to remove it.
pH by and large doesn't matter as long as it is stable and not at one extreme or the other. Fluctuating pH levels can harm the fish.
Hardness - there is only one real way to lower this and that's to use RO water (reverse osmosis, water that has had all the minerals removed) either by mixing it with hard tapwater or by using just RO with some minerals added back. Raising it is easier, you just add more minerals.
Hardness is actually more important than pH. Provided hardness is at the right end of the scale for a species, pH can be quite a bit off the 'desired' range. So looking at your fish list - neons and cardinals prefer soft acid water; guppies, mollies and platies prefer hard alkaline water; and silver tips, cherry barbs, and Indian gouramis (aka banded gouramis, Trichogaster fasciata) can tolerate both.
The problem with a lot of shops is that what they mean by good isn't necessarily what we mean by good
Once we know what your readings and hardness are, we'll be able see better if there is anything wrong.
Is your partner's uncle a member on here?
