You will need tests for Ammonia and Nitrites for the initial cycling of the tank.
You will need to have an idea of what the Gh and Kh of your tap water (assuming you are going to use tap water) and tank water is, as some plants need a low Gh and Kh. Once you have an idea, these typically don't change drastically, they will creep up or down slowly over time.
After that, you may decide to test Nitrates and Phospates. Beware that the tests kits can vary and may not be accurate. Because of this, it's best to calibrate them so you know how accurate they are. If you choose to go with the EI method of fertilization, you don't have to test, but you do large water changes each week (50%).
Again though, any test kit (ammonia, nitrite, Gh, Kh, Phosphate, Nitrate) has error in them and are only a rough idea. There is no standard inexpensive test for Potassium.
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