I have extensive training on testing water quality, but I don't do it in our fish room. One of these days I'll measure pH in our tanks! Just look at the tank. If the fish don't look right, you need to do a water change. If the water doesn't look or smell right, do a water change. Use a good water conditioner like prime or safe on the new water.
That said, I would argue the most important value to know is nitrite. It should be zero. If it is non-zero, you are either at the start of the cycling process or you have a problem. If you have an ammonia problem, you can smell it. Nitrite is more of a silent killer and is really only detectable without a kit by symptoms in the fish (heavy breathing and listlessness). Hanna makes a relatively cheap colorimeter for nitrite (
link). This tester is far better than the API master kit. But again... anything non-zero and it's time for action... so does it really matter exactly what the value is?
If you REALLY want to test for nitrate, Hanna has a cheap color based method that is better than the API master kit... you may recognize this sort of thing from pool test kits (
link). It is better because the color scale by which you judge the sample changes colors WITH the sample as the amount of light hitting both the sample and the color strip changes. Hanna also makes a fairly cheap handheld photometer (
link), but we're talking about spending money like a reefer now. The photometer is not as easy to use, but it is expandable, unlike the colorimeter (
link). If you are going to do much expanding... i.e. you want to measure a bunch of variables, there are better (cheaper) instruments available.
