I'm wondering if part of your question might be, which "tests" are necessary? For either planted or non-planted aquaria, a pH test is probably the single most important; for non-planted, a nitrate test may be more significant. The nitrate and/or pH tests if done regularly (e.g., each week prior to the water change) will let you know if there are changes from week to week which (when significant) usually mean something is wrong. Falling pH or rising nitrates can lead to serious fish problems.
At the beginning of a new aquarium, a test for ammonia and nitrite is very useful; it is good to have these on hand, but if regular maintenance (partial water changes) are carried out, you don't overstock or overfeed, and don't add too many fish at once, you may never need them. The API test kit combo includes pH, ammonia, nitrite and nitrate, and I believe the regents are reliable for 2-3 years.
A hardness test kit is not in my view essential; once you know the hardness of your tap water, there isn't much need for this test, unless you decide to soften/harden your water in the aquarium. Your local water board may be able to tell you the hardness of your tap water and what minerals are in it, and some fish stores will do this test.
Planted tank aquarists sometimes use test kits for CO2, iron, various nutrients. I don't bother; I'm not sure how reliable some of these are, plus you can gage all of this best by the plant growth itself. When one starts doing these various tests, it often leads to thinking this or that is lacking when in fact it may not be, and then un-necessary additives start going into the tank. The less chemicals in an aquarium, the better. IMHO.
I personally use API test kits, but I also have a Tetra low pH kit (the only one down to pH 5 that I have yet found locally).