For those with budget concerns. The fw kits generally needed in order of importance are:
Ammonia
Nitrite
pH
KH
GH
Nitrate
Kits also exist for testing special things such as phosphates, co2, iron etc. Most of these are not needed except by the real plant nuts.
Ammonia and nitrite kits are essential whether cycling or to have on hand for an established tank. pH is advisable since it can change over time and effects the toxicity of both ammonia and nitrite. However, pH and the other kits tend to be used way less than the first two. GH and KH are good to know but having your store check them is usually enough for most folks to need. Nitrate kits are fun but the least accurate and the least useful to most fw keepers. The plant nuts sometimes use this kit to help maintain a ratio between phosphate (they would have this kit too) and nitrate.
It is very helpful to know your tap water levels for all 6 kits at the outset since it is departures from those numbers, by how much and in what direction, that we will use to assess things in a tank when necessary. Even if you don;t buy all the kits, let your store test so you know your tap levels. You could also ask a friend who also keeps fish to help on this front if they have the kits.