When setting up any aquarium you need kits to test for-
Ammonia (NH3/4)
Nitrite (NO2)
Nitrate (NO3)
pH
Hardness (GH, KH)
The first two kits are vital to ensure your bio-filtration is effective. NO3 is important as high levels i.e. > 30ppm are harmful to fish. High NO3 is common in heavily stocked, low planted, under-maintained tanks, or those with high NO3 tap water.
pH and hardness (KH and GH) kits are a good idea to determine water chemistry. This allows you to stock suitable fish and plants. Do your research before buying any fish or plant is my recommendation. If you add CO2 then KH is cross referenced to pH to determine CO2 levels using a CO2 table.
If or when you get lots of heavy plant growth brought about by lots of light and CO2 injection then low NO3 may become an issue as the plants use it as a source of nitrogen which is a major plant nutrient (known as a macronutrient).
Phosphate (PO4) kits are useful. Too high may cause algae if you are not planted heavily with enough growth and too low can cause deficiencies.
I can recommend Nutrafin test kits in most instances, cheap and reliable enough for the majority of hobbyists.
Testing for ammonia and nitrite shouldn't be necessary after the filter has established. Testing regularly for pH and nitrate is a good idea to spot any negative trends before they adversely effect water quality. However a healthy, well-maintained planted aquarium will rarely suffer from any water quality issues. By creating a healthy environment for our plants we are doing the same for our fish. Plants are fantastic water purifiers, they even produce anti-biotics and allelochemicals that fend off algae.