Basically just adding my concurrence. But to your initial question, the Sera tests are probably the most reliable, but also more expensive. API are reliable and less cost, and I like many here use them.
As for testing, you should always do this at home. Just before the weekly partial water change is a good time, as the tank has been running for a week and you will get a better reading of things. The time of day matters for pH tests as pH fluctuates during the day/night so always testing pH at the same time of day is important to see if it is fluctuating generally. Daylight (but not direct sunlight) should be used to compare colours of water to the charts.
Ammonia and nitrite are useful during the initial stages of an aquarium, or if something seems wrong (like fish start dying or getting sick, or water clouds) it is good to test these. But once the tank is established, there should be no need for regular/frequent tests for ammonia or nitrite.
The pH and nitrate should be tested periodically, or subject to developments. Both can be signs of trouble. Also, pH may naturally lower as the biology progresses and this may affect fish depending upon the species.
Testing GH and KH is not necessary unless you are specifically targeting these, by which I mean if you are deliberately softening or hardening the water in a given tank. The tap water GH and KH and pH should always be known before setting up any aquarium, the GH and KH data can come from the water supply folks without you spending money on a test kit that will never be used again. You should also test the tap water for ammonia, nitrite and nitrate at the start. Generally speaking, GH and KH should not alter in the aquarium unless again you are targeting them somehow.