Welcome to Tropical Fish Keeping.
I agree with Boredomb, though here I would say you could live without ammonia and nitrite if you plant the tank well and go easy on introducing fish, and are regular with partial water changes [hope these are not too much work for you.
]. It has been years since I have tested either ammonia or nitrite. Nitrate is useful, periodically, as it can indicate pending trouble. The pH test is similar. Generally speaking, I only test for pH, and that only a few times a year unless I am fiddling with water parameters. Nitrates never vary in my tanks now, so maybe once or twice a year, but the result is always the same.
The GH is crucial to know, both for fish and plants, but a test kit is not necessary unless one is going to be adjusting the GH. Ascertaining the GH of your tap water from the municipal water people is sufficient. The should also know the pH, which will get you started.