If your in the initial stages of cycling and you want to know ammonia and nitrite, API is fine.
Once the tank is cycled, there are biological indicators of what your nitrate and phosphate levels are- such as green film, hair algae and macro algaes all growing. Algae takes up the nutrients in the water column into their tissues, so even if your phosphate reading might be zero, it's still present but is now in organic forms and not in the water column.
As you get more into the hobby and start to add corals, you might want to know where your calcium, alkalinity and magnesium sits. Salifert is a medium grade test kit. Seachem is better for me to use. It's a personal preference.
Hanna makes portable spectrophotometers that are expensive to buy and expensive to use, but they are pretty accurate.
I think my pocket pH probe is going to be fun to use.